  We study the role that the future detection of the neutrino burst from a
galactic supernova can play in the reconstruction of the neutrino mass
spectrum. We consider all possible 3$\nu$ mass and flavor spectra which
describe the solar and atmospheric neutrino data. For each of these spectra we
find the observable effects of the supernova neutrino conversions both in the
matter of the star and the earth. We show that studies of the electron neutrino
and anineutrino spectra as well as observations of the neutral current effects
from supernova will allow us (i) to identify the solar neutrino solution, (ii)
to determine the type of mass hierarchy (normal or inverted) and (iii) to probe
the mixing $|U_{e3}|^2$ to values as low as $10^{-4} - 10^{-3}$.
