  We consider type IIB $SL(2,\mathbb{Z})$ symmetry to relate the partition
functions of different 5d supersymmetric Abelian linear quiver Yang-Mills
theories in the $\Omega$-background and squashed $S^5$ background. By Higgsing
S-dual theories, we extract new and old 3d mirror pairs. Generically, the
Higgsing procedure yields 3d defects on intersecting spaces, and we derive new
hyperbolic integral identities expressing the equivalence of the squashed $S^3$
partition functions with additional degrees of freedom on the $S^1$
intersection.
