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 ( sSFR ) , 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 . In contrast , the star formation in the Mice , specially in Mice B , is not enhanced but inhibited with respect to Sbc–Sc MSSF galaxies . The fact that the gas fraction of Mice B is smaller than in most non-interacting spirals , and that the Mice is close to a prograde orbit , represents a new challenge for the models , which must cover a larger space of parameters in terms of the the availability of gas and the orbital characteristics .