In this letter we study topological open string field theory on D--branes in a IIB background given by non compact CY geometries O(n)⊕O(−2−n) on $P1$ with a singular point at which an extra fiber sits. We wrap N D5-branes on $P1$ and M effective D3-branes at singular points, which are actually D5--branes wrapped on a shrinking cycle. We calculate the holomorphic Chern-Simons partition function for the above models in a deformed complex structure and find that it reduces to multi--matrix models with flavour. These are the matrix models whose resolvents have been shown to satisfy the generalized Konishi anomaly equations with flavour. In the n=0 case, corresponding to a partial resolution of the A2 singularity, the quantum superpotential in the N=1 unitary SYM with one adjoint and M fundamentals is obtained. The n=1 case is also studied and shown to give rise to two--matrix models which for a particular set of couplings can be exactly solved. We explicitly show how to solve such a class of models by a quantum equation of motion technique.
