By applying multiplicate forms of the Carlitz inverse series relations to the $q$-Pfaff-Saalsch{ü}tz summation theorem, we establish twenty five nonterminating $q$-series identities with several of them serving as $q$-analogues of infinite series expressions for $π$ and $1/π$, including some typical ones discovered by Ramanujan (1914) and Guillera.