Morita equivalence for quantum Heisenberg manifolds

We discuss Morita equivalence within the family $\{D_{\mu\nu}^c: c\in \mathbb{Z} , c>0, \mu,\nu\in\mathbb{R}\}$ of quantum Heisenberg manifolds. Morita equivalence classes are described in terms of the parameters $\mu$, $\nu$ and the rank of the free abelian group $G_{\mu\nu}=2\mu\mathbb{Z} +2\nu\mathbb{Z} +\mathbb{Z}$ associated to the $C^*$-algebra $D_{\mu\nu}^{c}$.