  We critically analyze the claims with regard to the relevance of topological
phases in the physics of neutrino oscillation made in a recent paper [Phys.
Rev. D 79, 096013 (2009)] and point out some inappropriate exaggerations and
misleading statements. We find that the $\pi$ phase described in this paper,
while interesting, is an artefact of two major approximations made in the
paper. We point out a more robust and more familiar $\pi$ phase in the neutrino
oscillation formulae which can be interpreted as a pure Pancharatnam phase. We
also make some relevant remarks on the distinction between the geometric and
the topological phase made in the commented paper.
