  We study the integral Bailey lemma associated with the $\mathrm{A_n}$-root
system and identities for elliptic hypergeometric integrals generated thereby.
Interpreting integrals as superconformal indices of four-dimensional
$\mathcal{N}=1$ quiver gauge theories with the gauge groups being copies of
$\mathrm{SU(n+1)}$, we provide evidence for various new dualities. Further
confirmation is achieved by explicitly checking that the `t Hooft anomaly
matching conditions holds. We discuss a flavour symmetry breaking phenomenon
for supersymmetric quantum chromodynamics (SQCD), and by making use of the
Bailey lemma we indicate its manifestation in a web of linear quivers dual to
SQCD that exhibits full s-confinement.
