Accessibility and ergodicity for collapsed Anosov flows

We consider a class of partially hyperbolic diffeomorphisms introduced by the authors with Barthelm\'{e} which is open and closed and contains all known examples. If in addition the diffeomorphism is non-wandering, then we show it is accessible unless it contains a $su$-torus. This implies that these systems are ergodic when they preserve volume, confirming a conjecture by Hertz-Hertz-Ures for this class of systems.