  We report on our analysis of the 2019 outburst of the X-ray accreting pulsar
4U 1901+03 observed with Insight-HXMT and NICER. Both spectra and pulse
profiles evolve significantly in the decaying phase of the outburst. Dozens of
flares are observed throughout the outburst. They are more frequent and
brighter at the outburst peak. We find that the flares, which have a duration
from tens to hundreds of seconds, are generally brighter than the persistent
emission by a factor of $\sim$ 1.5. The pulse profile shape during the flares
can be significantly different than that of the persistent emission. In
particular, a phase shift is clearly observed in many cases. We interpret these
findings as direct evidence of changes of the pulsed beam pattern, due to
transitions between the sub- and super-critical accretion regimes on a short
time scale. We also observe that at comparable luminosities the flares' pulse
profiles are rather similar to those of the persistent emission. This indicates
that the accretion on the polar cap of the neutron star is mainly determined by
the luminosity, i.e., the mass accretion rate.
