We give a sequence of combinatorial models (CDGAs) for the Orlik-Solomon algebra of a matroid, arising from a sequence of combinatorial blowups. In the case that the matroid is complex realizable, each is a model in the sense of rational homotopy theory, arising from the Leray spectral sequence associated to the inclusion of the projective complement into a certain projective variety. This is joint work with Graham Denham and Eva Maria Feichtner.