  We compare previously found finite-dimensional matrix and integral operator
realizations of the Bailey lemma employing univariate elliptic hypergeometric
functions. With the help of residue calculus we explicitly show how the
integral Bailey lemma can be reduced to its matrix version. As a consequence,
we demonstrate that the matrix Bailey lemma can be interpreted as a
star-triangle relation, or as a Coxeter relation for a permutation group.
