It is known that if $f:M\rightarrow N$ is a homotopy equivalent, then the the process of pullback gives a one-one correspondence between bundles over $N$ and $M$ up to isomorphism. Is the converse( that if $f$ gives a 1-1 correspondence between them, then $f$ is a homotopy equivalence)true? Or any counterexample?

By the way, can we determine all the bundles over a certain kind of manifold, for example, compact one?

(I post it using my cellphone and it displays a little wierd. Does the page turn out fine in computer?)