We present the first calculations with three flavors of collective and shock wave effects for neutrino propagation in core-collapse supernovae using hydrodynamical 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.