I notice there is a strong connection between shellability of simplicial complexes and bistellar flips on these complexes; in particular, adding in a new facet of a shelling induces a bistellar flip on the boundary.

Is it always the case that bistellar flips preserve shellability of a complex? In other words, if I apply a bistellar flip to a shellable simplicial complex, is the resulting simplicial complex also shellable? If so, how can this be seen easily?