Restriction of a line bundle to a a two-cycle

Question

I am reading a paper on Chiral Differential Operators

http://arxiv.org/pdf/hep-th/0604179v3.pdf

and it says on page 23 that a line bundle over a manifold $C$ can be characterized completely by its restriction to a non-trivial two-cycle, such as a two-sphere in $C$.

The paper refers a book to check this fact: "Differential Forms in Algebraic Topology" by Raoul Bott & Loring W. Tu.

http://www.amazon.com/Differential-Algebraic-Topology-Graduate-Mathematics/dp/0387906134

I could not find any help from the book.

Edit: I have asked the same question on mathoverflow.net https://mathoverflow.net/questions/153772/restriction-of-a-line-bundle-to-a-two-cycle