Sentence:  In the Steiners have busy lives without visiting relatives only context can indicate whether visiting relatives is equivalent in meaning to paying visits to relatives or to relatives who are visiting them , and in I looked up the number and I looked up the chimney only the meanings of number and <WSD>chimney</WSD> make it clear that up is syntactically a second complement in the first sentence and a preposition followed by its object in the second . 
Meaning of the word marked with <WSD> tags:  a vertical flue that provides a path through which smoke from a fire is carried away through the wall or roof of a building