  We consider two cases of birational transformations of Q-Gorenstein
threefolds: the case of a terminal flop and the case of a Francia flip.
  In the first case we show that, if one replaces the threefolds by their
canonical covering stacks, the the flop coincides with the moduli stack of
perverse point sheaves. This adds to a result of Kawamata showing the derived
equivalence. Our construction has the drawback that the moduli space is defined
using a presentation of the stack.
  In the second case we show that, if one takes a Francia flip $X \to Y$ and
replaces $X$ by its canonical covering stack, then the flip coincides with a
version of Bridgelan'd moduli space of pewrverse point sheaves involving a new
perversity. This adds to another result of Kawamata. Again there is a drawback
- the proof of the result relies on the existence of the flip, in contrast with
the results of Bridgeland and of Chen where the relevant flop appears as an
outcome of the construction.
