Question: What railway routes connecting two major cities in the North West of England are included in the City Line?

Context paragraphs:
City Line (Merseyrail): The City Line is the name given to local rail routes out of Liverpool Lime Street railway station.  It appears on maps of the Merseyrail network as red, and covers the Liverpool–Wigan line as well as the two routes of the Liverpool–Manchester lines.  Although it is branded under the Merseyrail name, the routes are operated by Northern on behalf of Merseytravel rather than by the Merseyrail franchise.

Race to the North: The Race to the North was the name given by the press to occasions in two summers of the late 19th century when British passenger trains belonging to different companies would literally race each other from London to Scotland over the two principal rail trunk routes connecting the English capital city to Scotland – the West Coast Main Line which runs from London Euston via Crewe and Carlisle and the East Coast Main Line route from London King's Cross via York and Newcastle.  The "races" were never official and publicly the companies denied that what happened was racing at all.  Results were not announced officially and the outcomes have since been hotly debated.  In the 20th century there were also occasions of competition for speed on the two routes.

Southern Railway routes west of Salisbury: This article describes the history and operation of the railway routes west of Salisbury built by the London and South Western Railway (LSWR) and allied companies, which ultimately became part of the Southern Railway in the United Kingdom.  Salisbury forms a natural boundary between the Southern Railway core routes in the counties surrounding London, and the long route connecting with the Devon and Cornwall lines.

London and South Western Railway: The London and South Western Railway (LSWR) was a railway company in England from 1838 to 1922.  Starting as the London and Southampton Railway, its network extended from London to Plymouth via Salisbury and Exeter, with branches to Ilfracombe and Padstow and via Southampton to Bournemouth and Weymouth.  It also had many routes connecting towns in Hampshire and Berkshire, including Portsmouth and Reading.  In the grouping of railways in 1923 the LSWR amalgamated with other railways to create the Southern Railway.

Yiwu-London railway line: The Yiwu – London Railway Line is a freight railway route from Yiwu, China, to London, United Kingdom, covering a distance of roughly 12,000 km (7,456 miles).  This makes it the longest railway freight route in the world.  It is one of several long distance freight railway routes from China to Europe on the “New Eurasian Land Bridge” and part of establishing a modern-day Silk Road.  The route was opened on the 1st of January 2017, making London the 15th European city to have a railway route connection with China, and takes 18 days to complete (other European cities with China-Europe railway routes include Hamburg, Madrid, Rotterdam, Warsaw, etc.).

Jamaica–Far Rockaway line: The Q111, Q113, and Q114 bus routes constitute a public transit line between the Jamaica and Far Rockaway neighborhoods of Queens, New York City, United States, running primarily along Guy R. Brewer Boulevard.  The Q113 and Q114 provide limited-stop service between Jamaica and Far Rockaway, connecting two major bus-subway hubs, and crossing into Nassau County.  The Q111 provides local service exclusively within Queens, with the exception of select rush-hour trips to or from Cedarhurst in Nassau County.  Some of the last bus routes to be privately operated in the city, they are currently operated by the MTA Bus Company brand of MTA Regional Bus Operations.  The Q113 and Q114 are one of the few public transit options between the Rockaway peninsula and "mainland" New York City.

West Coast Main Line: The West Coast Main Line (WCML) is one of the most important railway corridors in the United Kingdom, connecting the major cities of London, Birmingham, Glasgow, Liverpool and Manchester.  It is one of the busiest mixed-traffic railway routes in Europe, carrying a mixture of intercity rail, regional rail, commuter rail and rail freight traffic.  The core route of the WCML runs from London to Glasgow, with branches diverging to Birmingham, Manchester and Liverpool, totalling a route mileage of 700 mi .  Services from London to North Wales and Edinburgh also run via the WCML; however the main London-Edinburgh route is the East Coast Main Line.  In addition, several sections of the WCML form part of the suburban railway systems in London, Birmingham, Manchester and Glasgow, with many more smaller commuter stations, as well as providing links to more rural towns.

Liverpool–Manchester lines: There were once four direct railway routes between Liverpool and Manchester in the North West of England.  There are now only two remaining direct railway routes between the two cities.  One line, the now northern route, is fully electric and the other, the southern route, is a diesel only line.  A third line which is further north has been split with the western section electric and the eastern section diesel operation, requiring a passenger change between the two cities.  The fourth route, the most southerly, is largely abandoned east of Warrington with the remaining section mostly catering for freight trains.  The remaining two direct routes are:

Picc-Vic tunnel: Picc-Vic was a proposed, and later cancelled, underground railway designed in the early 1970s with the purpose of connecting two major mainline railway termini in Manchester city centre, England.  The name Picc-Vic was a contraction of the two station names, Manchester Piccadilly and Manchester Victoria.  The proposal envisaged the construction of an underground tunnel across Manchester city centre.  The scheme was abandoned in 1977 during its proposal stages due to excessive costs, and that the scheme still retained two large expensive to maintain terminal stations in Manchester; other similar sized cities had reduced their terminals to one.

Moscow-Kazan high-speed railway: The Moscow-Kazan High-Speed Railway is a 772-kilometre long high-speed railway line connecting the two major cities of Moscow and Kazan in the Russian Federation, going through the intermediate cities of Vladimir, Nizhny Novgorod and Cheboksary.  The project, currently being designed with an expected completion date of 2020, is slated to be the first segment of an ambitious transnational high-speed railway set to connect Beijing and Moscow over a distance in excess of 7,000 kilometres, which is currently under consideration by the governments of Russia and China.

Supporting paragraphs: City Line (Merseyrail) Liverpool–Manchester lines
Answer: Liverpool–Manchester lines