We present different transport measurements up to fields of 29~T in the recently discovered heavy-fermion superconductor UTe$_{2}$ with magnetic field $H$ applied along the easy magnetization a-axis of the body-centered orthorhombic structure. The thermoelectric power varies linearly with temperature above the superconducting transition, $T_{SC}= 1.5$ K, indicating that superconductivity develops in a Fermi liquid regime. As a function of field the thermolelectric power shows successive anomalies which are attributed to field-induced Fermi surface instabilities. These Fermi-surface instabilities appear at critical values of the magnetic polarization. Remarkably, the lowest magnetic field instability for $Hparallel a$ occurs for the same critical value of the magnetization (0.4 $mu_B$) than the first order metamagnetic transition at 35~T for field applied along the $b$-axis. The estimated number of charge carriers at low temperature reveals a metallic ground state distinct from LDA calculations indicating that strong electronic correlations are a major issue in this compound.
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