They don't.
Except possibly under extremely intense conditions (starting with a spark gap anyway, to generate extreme dV/dt, then putting the MOVs or TVSs in a distributed transmission line structure), they have positive incremental resistance, so they just burn the power applied, no sharpening, no triggering.
A SIDAC or any other 4-layer semiconductor can be used instead, but these are typically slower, and relatively fragile in that they are made of semiconductor; the current flow may not distribute evenly within fractions of a microsecond. (They're usually rated for surge, getting similar ratings to other diodes and SCRs, good enough to clear a fuse in many cases, but still nowhere near the energy absorption of pure plasma, give or take how much electrode damage you consider acceptable of course.)
Tim