  Interpolated multiple $q$-zeta values are deformation of multiple $q$-zeta
values with one parameter, $t$, and restore classical multiple zeta values as
$t = 0$ and $q \to 1$. In this paper, we discuss generating functions for sum
of interpolated multiple $q$-zeta values with fixed weight, depth and
$i$-height. The functions are systematically expressed in terms of the basic
hypergeometric functions. Compared with the result of Ohno and Zagier, our
result includes three generalizations: general height, $q$-deformation and
$t$-interpolation. As an application, we prove some expected relations for
interpolated multiple $q$-zeta values including sum formulas.
