I'm interested in computing - to the extent possible - the Leray spectral sequence for a particular map which is *almost*, but not quite, a fiber bundle (e.g. a Seifert fiber space). The hardest step currently is writing down the edge maps on the $E\_2$ page.


Can someone point me to a reference that derives the Leray sequence from a topological/geometric point of view (i.e. not by appealing to the Grothendieck spectral sequence)? I recall reading somewhere that a CW-structure on the base space can induce the needed filtration, but the reference I found (which I can't remember now) only did this for the case of an actual fiber bundle.



Topological Derivation of Leray Spectral Sequence
[Bott and Tu](http://www.maths.ed.ac.uk/~aar/papers/botttu.pdf) do this in their book *Differential forms in algebraic topology*, see Section 14, ``Leray's construction" (starting on page 179).


