  We show that the phase appearing in neutrino flavor oscillation formulae has
a geometric and topological contribution. We identify a topological phase
appearing in the two flavor neutrino oscillation formula using Pancharatnam's
prescription of quantum collapses between non-orthogonal states. Such quantum
collapses appear naturally in the expression for appearance and survival
probabilities of neutrinos. Our analysis applies to neutrinos propagating in
vacuum or through matter. For the minimal case of two flavors with CP
conservation, our study shows for the first time that there is a geometric
interpretation of the neutrino oscillation formulae for the detection
probability of neutrino species.
