Over the past two decades, strong evidence that galaxies have undergone a significant evolution over cosmic time were found. Do galaxy mergers, one of the main driving mechanisms behind the growth of galaxies, played a key role in their evolution at significant look-back time? Due to the difficulty to identify these violent interactions between galaxies at high redshifts, the major merger rate, involving two galaxies of similar masses, was constrained so far up to redshift z~3, from previous studies of spectrocopic pair counts. Thanks to MUSE, which is perfectly suited to identify close pairs of galaxies with secure spectroscopic redshifts, we are now able to extend such studies up to z~6. I will present the results obtained from deep (10-30h) MUSE observations in the Hubble Ultra Deep Field. We provide the first constraints on the galaxy major merger evolution over 12 Gyrs (0.2 < z < 6) and over a broad range of stellar masses, showing that there is a flattening of the major merger rate evolution at very high redshift.