  Geometric (Aharonov--Anandan) phases in neutrino oscillations have been
claimed [Phys. Lett. B 780 (2018) 216] to be sensitive to the Majorana phases
in neutrino mixing. More recently, however, it has been pointed out [Phys.
Lett. B 818 (2021) 136376] that the proposed phases are not gauge invariant.
Using both kinematic and geometric approaches, we show that all gauge-invariant
Aharonov--Anandan phases (including the off-diagonal geometric phases
associated with flavor transitions) are independent of the Majorana phases.
This finding, which generalizes the well-known fact that conventional
oscillation experiments cannot discern the Dirac or Majorana nature of the
neutrino, implies that a hypothetical interference experiment cannot
distinguish between the two either.
