Right, thank you, I was confused. Then, how would you justify that the Leray spectral seuence works for seifert bundles? I thought it just worked for fibrations...

Ok, sorry I didn't know this was not OK. Then I could delete the stack exchange question.

I just edited the question saying that I have a partial answer, don't know what do you mean.

I don't see this implication: "Finally if χ(Xk)<0, then it is a connected sum of a torus with some number of projective planes. So it has non-orientable covers of all degrees; these are determined by their Euler characteristics." How can I construct that coverings? Is that a known result that I can find in some book or something? In the case of orientable surfaces it is easy to construct the coverings because it is a kind of glue-rotation, but in this case I can't visualize anything. Thank you!