  We show that neutrino spin and spin-flavor transitions involve nonvanishing
geometric phases. The geometric character of neutrino spin rotation is explored
by studying the neutrino spin trajectory in the projective Hilbert space
representation and its relation to the geometric phase. Analytical expressions
are derived for noncyclic geometric phases. Several calculations are performed
for different cases of rotating and nonrotating magnetic fields in the context
of solar neutrinos and neutrinos produced inside neutron stars. Also the
effects of adiabaticity, critical magnetic fields and cross boundary effects in
the case of neutrinos emanating out of neutron stars are examined.
