  We present the first calculations with three flavors of collective and shock
wave effects for neutrino propagation in core-collapse supernovae using
hydroynamical density profiles and the S matrix formalism. We explore the
interplay between the neutrino-neutrino interaction and the effects of multiple
resonances upon the time signal of positrons in supernova observatories. A
specific signature is found for the inverted hierarchy and a large third
neutrino mixing angle and we predict, in this case, a dearth of lower energy
positrons in Cherenkov detectors midway through the neutrino signal and the
simultaneous revelation of valuable information about the original fluxes. We
show that this feature is also observable with current generation neutrino
detectors at the level of several sigmas.
