I think that you have to investigate in the direction of [fibrations][1].
And then, maybe, [spectral sequences][2].

edit: Concernig your comment -- I am interested in that as well.

Right now my investigation got me there -- check the book
*"Modern Geometry - Methods and Applications: Part 3: Introduction to Homology Theory"
by: B.A. Dubrovin, A.T. Fomenko, S.P. Novikov.*

Chapter 20.

It is quite difficult for me to read the book (Yeah, you got me, I'm a physicist.) so I cannot give you anything but the direction.

  [1]: http://en.wikipedia.org/wiki/Fibration
  [2]: http://en.wikipedia.org/wiki/Serre_spectral_sequence