  AGT relations imply that the four-point conformal block admits a
decomposition into a sum over pairs of Young diagrams of essentially rational
Nekrasov functions - this is immediately seen when conformal block is
represented in the form of a matrix model. However, the q-deformation of the
same block has a deeper decomposition - into a sum over a quadruple of Young
diagrams of a product of four topological vertices. We analyze the interplay
between these two decompositions, their properties and their generalization to
multi-point conformal blocks. In the latter case we explain how Dotsenko-Fateev
all-with-all (star) pair "interaction" is reduced to the quiver model
nearest-neighbor (chain) one. We give new identities for q-Selberg averages of
pairs of generalized Macdonald polynomials. We also translate the slicing
invariance of refined topological strings into the language of conformal blocks
and interpret it as abelianization of generalized Macdonald polynomials.
