  We present a framework for the study of $q$-difference equations satisfied by
$q$-semi-classical orthogonal systems. As an example, we identify the
$q$-difference equation satisfied by a deformed version of the little
$q$-Jacobi polynomials as a gauge transformation of a special case of the
associated linear problem for $q$-$\mathrm{P}_{\mathrm{VI}}$. We obtain a
parameterization of the associated linear problem in terms of orthogonal
polynomial variables and find the relation between this parameterization and
that of Jimbo and Sakai.
