  It is shown that the neutron-antineutron oscillation per se does not
necessarily imply CP violation in an effective local Lorentz invariant
description of the neutron which preserves CPT, contrary to a recent analysis
in the literature. A CP- and baryon number-violating term can be transformed
into a CP conserving one, thus rendering the CP violation spurious and unusable
in the analysis of baryogenesis, for example. It is also shown that the
neutron-antineutron oscillation in a $\Delta B=2$, Lorentz and CPT invariant
interaction can occur only when parity is violated, irrespective of the CP
properties; when parity is conserved, it is the ordinary quantum transition
from neutron to antineutron which takes place. Those statements are proven by
explicitly analyzing all the possible combinations with P, C and CP violation
or their conservation. Moreover, a suitable combination of P=odd and P=even
$\Delta B=2$ interactions in the present model is shown to give rise to the CP
preserving mass term for the right-handed neutrino if one replaces the neutron
by the neutrino, reinforcing the conclusion.
