  We glue four refined topological vertices to obtain the building block of 5D
$U(2)$ quiver instanton partition functions. We take the 4D limit of the result
to obtain the building block of 4D instanton partition functions which, using
the AGT correspondence, are identified with Virasoro conformal blocks.
  We show that there is a choice of the parameters of the topological vertices
that we start with, as well as the parameters and the intermediate states
involved in the gluing procedure, such that we obtain Virasoro minimal model
conformal blocks.
