  Self-induced flavor conversions near the supernova (SN) core can make the
fluxes for different neutrino species become almost equal, potentially altering
the dynamics of the SN explosion and washing out all further neutrino
oscillation effects. We present a new model-independent analysis strategy for
the next galactic SN signal that will distinguish this flavor equalization
scenario from a matter effects only scenario during the SN accretion phase. Our
method does not rely on fitting or modelling the energy-dependent fluences of
the different species to a known function, but rather uses a model-independent
comparison of charged-current and neutral-current events at large
next-generation underground detectors. Specifically, we advocate that the
events due to elastic scattering on protons in a scintillator detector, which
is insensitive to oscillation effects and can be used as a model-independent
normalization, should be compared with the events due to inverse beta decay of
$\bar\nu_e$ in a water Cherenkov detector and/or the events due to
charged-current interactions of $\nu_e$ in an Argon detector. The ratio of
events in these different detection channels allow one to distinguish a
complete flavor equalization from a pure matter effect, for either of the
neutrino mass orderings, as long as the spectral differences among the
different species are not too small.
