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.