  We study certain six dimensional theories arising on $(p,q)$ brane webs
living on $\mathbb{R}\times S^1$. These brane webs are dual to toric
elliptically fibered Calabi-Yau threefolds. The compactification of the space
on which the brane web lives leads to a deformation of the partition functions
equivalent to the elliptic deformation of the Ding-Iohara algebra. We compute
the elliptic version Dotsenko-Fateev integrals and show that they reproduce the
instanton counting of the six dimensional theory.
