  We give an explicit description of the Bott-Chern cohomology groups of a
compact Vaisman manifold in terms of the basic cohomology. We infer that the
Bott-Chern numbers and the Dolbeault numbers of a Vaisman manifold determine
each other. On the other hand, we show that the cohomological invariants
$\Delta^k$ introduced by Angella-Tomassini are unbounded for Vaisman manifolds.
Finally, we give a cohomological characterization of the Dolbeault and
Bott-Chern formality for Vaisman metrics.
