Framed holomorphic bundles on rational surfaces

We study the moduli space of framed holomorphic bundles of any rank, over the blow-up of CP2 at q points. For c(2) = 1; 2 we introduce an open cover of the moduli space and describe its nerve. In the limit when r -> infinity we use this result to obtain the homotopy type of the moduli spaces. In particular, we compute the cohomology of the moduli spaces.