  Neutrino oscillations are one of the first evidences of physics beyond the
Standard Model (SM). Since Lorentz Invariance is a fundamental symmetry of the
SM, recently also neutrino physics has been explored to verify the eventual
modification of this symmetry and its potential magnitude. In this work we
study the consequences of the introduction of Lorentz Invariance Violation
(LIV) in the high energy neutrinos propagation and evaluate the impact of this
eventual violation on the oscillation predictions. An effective theory
explaining these physical effects is introduced via Modified Dispersion
Relations. This approach, originally introduced by Coleman and Glashow,
corresponds in our model to a modification of the special relativity geometry.
Moreover, the generalization of this perspective leads to the introduction of a
maximum attainable velocity which is specific of the particle. This can be
formalized in Finsler geometry, a more general theory of space-time. In the
present paper the impact of this kind of LIV on neutrino phenomenology is
studied, in particular by analyzing the corrections introduced in neutrino
oscillation probabilities for different values of neutrino energies and
baselines of experimental interest. The possibility of further improving the
present constraints on CPT-even LIV coefficients by means of our analysis is
also discussed.
