  We study the effect of Majorana transition magnetic moments on the flavor
evolution of neutrinos and antineutrinos inside the core of Type-II supernova
explosions. We find non-trivial collective oscillation effects relating
neutrinos and antineutrinos of different flavors, even if one restricts the
discussion to Majorana transition electromagnetic moment values that are not
much larger than those expected from standard model interactions and nonzero
neutrino Majorana masses. This appears to be, to the best of our knowledge, the
only potentially observable phenomenon sensitive to such small values of
Majorana transition magnetic moments. We briefly comment on the effect of Dirac
transition magnetic moments and on the consequences of our results for future
observations of the flux of neutrinos of different flavors from a nearby
supernova explosion.
