at.algebraic topology - Mayer-Vietoris homotopy groups sequence of a pull-back of a fibration

A low level Mayer-Vietoris sequence for a pull-back of a fibration of groupoids is in
(R. BROWN, P.R. HEATH and H. KAMPS), ``Groupoids and the
Mayer-Vietoris sequence'', {em J. Pure Appl. Alg.} 30 (1983)

and you will also find a version for coverings of groupoids in
`Topology and Groupoids', R. Brown (available on amazon.com).

I've set as an exercise in my new coauthored book `Nonabelian algebraic topology' (see my web pages) to get a Mayer-Vietoris sequence for a pullback of a fibration of crossed complexes.