using MACRO data.

Neutrino-induced upward-going muons in MACRO have been analysed in terms of relativity principles violating effects, keeping standard mass-induced atmospheric neutrino oscillations as the dominant source of νμ → ντ transitions. The data disfavor these exotic possibilities even at a sub-dominant level, and stringent 90% C.L. limits are placed on the Lorentz invariance violation parameter |∆v| < 6× 10 at sin 2θv = 0 and |∆v| < 2.5 ÷ 5 × 10 at sin 2θv = ±1. These limits can also be re-interpreted as upper bounds on the parameters describing violation of the Equivalence Principle. Neutrino mass-induced oscillations are the best explanation of the atmospheric neutrino problem [1, 2, 3, 4]. Two flavor νμ → ντ oscillations are strongly favored over a wide range of alternative solutions such as νμ → νsterile oscillations [5, 6], νμ → νe oscillations [3, 4] or other exotic possibilities [7, 8]. In this letter, we assume standard mass-induced neutrino oscillations as the leading mechanism for flavor transitions and we treat Lorentz invariance flavor transitions as a sub-dominant effect [9]. In the literature, neutrino oscillations induced by Violation of (CPTconserving) Lorentz Invariance (VLI) and Violation of the Equivalence