  This paper presents the spatially resolved star formation history (2D-SFH) of
a small sample of four local mergers: the early-stage mergers IC1623, NGC6090,
and the Mice, and the more advanced merger NGC2623, by analyzing IFS data from
the CALIFA survey and PMAS in LArr mode. Full spectral fitting techniques are
applied to the datacubes to obtain the spatially resolved mass growth
histories, the time evolution of the star formation rate intensity
($\Sigma_{SFR}$), and the local specific star formation rate, over three
different timescales (30 Myr, 300 Myr, and 1 Gyr). The results are compared
with non-interacting Sbc--Sc galaxies, to quantify if there is an enhancement
of the star formation and to trace its time scale and spatial extent. Our
results for the three LIRGs (IC1623W, NGC6090, and NGC2623) show that a major
phase of star formation is occurring in time scales of 10$^{7}$ yr to few
10$^{8}$ yr, with global SFR enhancements of $\sim$2--6 with respect to
main-sequence star forming (MSSF) galaxies. In the two early-stage mergers
IC1623W and NGC6090, which are between first pericenter passage and
coalescence, the most remarkable increase of the SFR with respect to
non-interacting spirals occurred in the last 30 Myr, and it is spatially
extended, with enhancements of factors 2--7 both in the centres ($r <$ 0.5 half
light radius, HLR), and in the disks ($r >$ 1 HLR). In the more advanced merger
NGC 2623 an extended phase of star formation occurred on a longer time-scale of
$\sim$1 Gyr, with a SFR enhancement of a factor $\sim$2--3 larger than the one
in Sbc--Sc MSSF galaxies over the same period, probably relic of the first
pericenter passage epoch. A SFR enhancement in the last 30 Myr is also present,
but only in NGC2623 centre, by a factor 3. In general, the spatially resolved
SFHs of the LIRG-mergers are consistent with the predictions from high spatial
resolution simulations.
