  We formulate an alternative approach based on unitarity triangles to describe
neutrino oscillations in presence of non-standard interactions (NSI). Using
perturbation theory, we derive the expression for the oscillation probability
in case of NSI and cast it in terms of the three independent parameters of the
leptonic unitarity triangle (LUT). The form invariance of the probability
expression (even in presence of new physics scenario as long as the mixing
matrix is unitary) facilitates a neat geometric view of neutrino oscillations
in terms of LUT. We examine the regime of validity of perturbative expansions
in the NSI case and make comparisons with approximate expressions existing in
literature. We uncover some interesting dependencies on NSI terms while
studying the evolution of LUT parameters and the Jarlskog invariant.
Interestingly, the geometric approach based on LUT allows us to express the
oscillation probabilities for a given pair of neutrino flavours in terms of
only three (and not four) degrees of freedom which are related to the geometric
properties (sides and angles) of the triangle. Moreover, the LUT parameters are
invariant under rephasing transformations and independent of the
parameterization adopted.
