Mutliple mixing and disjointness for time changes of bounded-type Heisenberg nilflows

We study time changes of bounded type Heisenberg nilflows $({\varphi }_t)$ acting on the Heisenberg nilmanifold $M$. We show that for every positive $\tau\in W^s(M)$,$s~>~7/2$,everynon-trivialtimechange$(\phi_t^{\tau})$ enjoys the Ratner property. As a consequence every mixing time change is mixing of all orders. Moreover we show that for every $\tau \in W^s(M)$, $s>9\mathrm{/}2$ and every $p,q\in \mathbb{N}$, $p\mathrm{\ne }q$, $({\varphi }_{pt}^{\tau })$ and $({\varphi }_{qt}^{\tau })$ are disjoint. As a consequence Sarnak’s Conjecture on M"obius disjointness holds for all such time changes.