Question: Which was fought first, Battle of Tarawa or Spring 1945 offensive in Italy?

Context paragraphs:
LXXVI Panzer Corps: The LXXVI Panzer Corps ("LXXVI Panzerkorps", 76th Armoured Corps) was a panzer corps of Nazi Germany during World War II.  The headquarters were formed in France under Army Group D on 29 June 1943 as LXXVI Army Corps but renamed a month later.  In August it shipped to Italy to become part of 10th Army.  It spent the rest of the war in Italy fighting in the Italian Campaign mainly under 10th Army but with short periods from February 1944 (Battle of Anzio) and January 1945 (Spring 1945 offensive in Italy) under 14th Army.  The Corps was commanded for most of its active fighting by General Traugott Herr.

Rhodesian Armoured Corps: The Rhodesian Armoured Corps—the "Black Devils"—was the only standing armoured battalion of the Rhodesian Security Forces.  During World War II, it took part in the Allied Spring 1945 offensive and the Battle of Monte Cassino as part of South Africa's 6th Armoured Division.  The unit was among the first to enter a liberated Florence in July 1944.  Prior to 1963, its crews were trained in the United Kingdom or Aden Colony and were known as the "Selous Scouts" under the Federation of Rhodesia and Nyasaland.  After Rhodesia's Unilateral Declaration of Independence, maintaining the armoured vehicle fleet became a responsibility of the Rhodesian Light Infantry until Major Bruce Rooken-Smith reactivated the former "Rhodesian Armoured Car Regiment" in 1972.  During the Rhodesian Bush War, the regiment fought in several major campaigns and battles, particularly Operation Miracle in September 1979.  It was superseded by the new "Zimbabwe Armoured Corps" between 1980 and 1981.

USS Tarawa (CV-40): USS "Tarawa" (CV/CVA/CVS-40, AVT-12) was one of 24 "Essex"-class aircraft carrier s built during and shortly after World War II for the United States Navy.  The ship was the first US Navy ship to bear the name, and was named for the bloody 1943 Battle of Tarawa.  "Tarawa" was commissioned in December 1945, too late to serve in World War II.  After serving a short time in the Far East, she was decommissioned in 1949.  She was soon recommissioned after the Korean War began, serving in the Atlantic as a replacement for carriers sent to Korea.  In the early 1950s, she was redesignated an attack carrier (CVA) and then an antisubmarine warfare carrier (CVS).  Except for one tour in the Far East, she spent her entire second career operating in the Atlantic and Caribbean.  Consequently, "Tarawa" was the only ship of her class to never see combat action.

Spring 1945 offensive in Italy: The Spring 1945 offensive in Italy, codenamed Operation Grapeshot, was the final Allied attack during the Italian Campaign in the final stages of the Second World War.  The attack into the Lombardy Plain by the 15th Allied Army Group started on 6 April 1945, ending on 2 May with the formal surrender of German forces in Italy.

Battle of the Argenta Gap: The Battle of the Argenta Gap was an engagement which formed part of the Allied spring 1945 offensive during the Italian Campaign in the final stages of the Second World War.  It took place in northern Italy from 12–19 April 1945 between troops of British V Corps commanded by Lieutenant-General Charles Keightley and German units of LXXVI Panzer Corps commanded by Lieutenant General ("General der Panzertruppe") Gerhard von Schwerin.

Battle of Bologna: The Battle of Bologna was fought in Bologna, Italy from 9–21 April 1945 during the Second World War, as part of the Spring 1945 offensive in Italy.  The Allied forces were victorious, with the Polish II Corps and supporting Allied units capturing the city on 21 April.

Operation Roast: Operation Roast was a military operation undertaken by British Commandos, at Comacchio lagoon in north-east Italy, during the Spring 1945 offensive in Italy, part of the Italian Campaign, during the final stages of Second World War.

Operation Grapeshot order of battle: Operation Grapeshot order of battle is a listing of the significant formations that were involved in the Spring 1945 offensive in the Apennine Mountains and the Po valley in northern Italy, April 1945 – May 1945.

Battle of Tarawa: The Battle of Tarawa was a battle in the Pacific Theater of World War II that was fought on 20–23 November 1943.  It took place at the Tarawa Atoll in the Gilbert Islands, and was part of Operation Galvanic, the U.S. invasion of the Gilberts.  Nearly 6,400 Japanese, Koreans, and Americans died in the fighting, mostly on and around the small island of Betio, in the extreme southwest of Tarawa Atoll.

191st Army Band: The 191st Army Band, the "Band of the Wild West", is a military band of the U.S. Army Reserve posted at Camp Parks, California.  Activated in 1943 as the 91st Infantry Division Band, the unit deployed to Europe in World War II where it fought in the Spring 1945 offensive in Italy.  It received its current designation as the 191st Army Band in 2008.  The 191st Army Band is a subordinate unit of the U.S. Army's 63rd Regional Support Command.

Supporting paragraphs: Battle of Tarawa Spring 1945 offensive in Italy
Answer: Battle of Tarawa