TITLE: Mayer-Vietoris homotopy groups sequence of a pull-back of a fibration
QUESTION [5 upvotes]: This must be an elementary question: could somebody tell me a reference for the Mayer-Vietoris homotopy groups sequence of a pull-back of a fibration?
I'm working in the category of pointed simplicial sets. So I've a pull-back of a (Kan) fibration of pointed simplicial sets, and I've read that in this situation you have an associated Mayer-Vietoris sequence relating the homotopy groups of the simplicial sets of the pull-back that looks like the classical Mayer-Vietoris sequence for the singular homology of a pair of open sets covering a topological space.
I've been searching in May's "Simplicial objects in Algebraic Topology" and Goerss-Jardine's "Simplicial Homotopy Theory", but I couldn't find it.

REPLY [3 votes]: Here is a lower-tech version of Reid's answer.  In general, if one has a Serre fibration p: E->B, and a map f: X->B, then there is a Mayer-Vietoris type sequence that comes from weaving together the long exact sequences in homotopy associated to p and to f*(p): f*(E)->X.  These exact sequences agree on every third term, because the fibers of f*(p) and p are homeomorphic.  The weaving process I'm talking about is an exercise in Hatcher's book (Exercise 38 in Section 2.2).
The relation between this exact sequence and the usual Mayer-Vietoris sequence in cohomology is explained here: Mathematically mature way to think about Mayer–Vietoris