  We provide, for the first time, robust observational constraints on the
galaxy major merger fraction up to $z\approx 6$ using spectroscopic close pair
counts. Deep Multi Unit Spectroscopic Explorer (MUSE) observations in the
Hubble Ultra Deep Field (HUDF) and Hubble Deep Field South (HDF-S) are used to
identify 113 secure close pairs of galaxies among a parent sample of 1801
galaxies spread over a large redshift range ($0.2<z<6$) and stellar masses
($10^7-10^{11} M_\odot$), thus probing about 12 Gyr of galaxy evolution.
Stellar masses are estimated from spectral energy distribution (SED) fitting
over the extensive UV-to-NIR HST photometry available in these deep Hubble
fields, adding Spitzer IRAC bands to better constrain masses for high-redshift
($z\geqslant 3$) galaxies. These stellar masses are used to isolate a sample of
54 major close pairs with a galaxy mass ratio limit of 1:6. Among this sample,
23 pairs are identified at high redshift ($z\geqslant 3$) through their
Ly$\alpha$ emission. The sample of major close pairs is divided into five
redshift intervals in order to probe the evolution of the merger fraction with
cosmic time. Our estimates are in very good agreement with previous close pair
counts with a constant increase of the merger fraction up to $z\approx 3$ where
it reaches a maximum of 20%. At higher redshift, we show that the fraction
slowly decreases down to about 10% at $z\approx6$. The sample is further
divided into two ranges of stellar masses using either a constant separation
limit of $10^{9.5} M_\odot$ or the median value of stellar mass computed in
each redshift bin. Overall, the major close pair fraction for low-mass and
massive galaxies follows the same trend.
  These new, homogeneous, and robust estimates of the major merger fraction
since $z\approx6$ are in good agreement with recent predictions of cosmological
numerical simulations.
