On Bailey pairs for $N$ = 2 supersymmetric gauge theories on ${S}_{b}^{3}/{ℤ}_{r}$

We study Bailey pairs construction for hyperbolic hypergeometric integral identities acquired via the duality of lens partitions functions for the three-dimensional $N$ = 2 supersymmetric gauge theories on ${S}_{b}^{3}/{ℤ}_{r}$ . The novel Bailey pairs are constructed for the star-triangle relation, the star-star relation, and the pentagon identity. The first two of them are integrability conditions for the Ising-type integrable lattice models. The last one corresponds to the representation of the basic 2 − 3 Pachner move for triangulated 3-manifolds.