  We present the first search for galaxy counterparts of intervening high-z
(2<z< 3.6) sub-DLAs and DLAs towards GRBs. Our final sample comprises of five
intervening sub-DLAs and DLAs in four GRB fields. To identify candidate galaxy
counterparts of the absorbers we use deep optical and near-infrared imaging,
and low-, mid- and high-resolution spectroscopy acquired with 6 to 10-m class
telescopes, the Hubble and the Spitzer space telescopes. Furthermore, we use
the spectroscopic information and spectral-energy-distribution fitting
techniques to study them in detail. Our main result is the detection and
spectroscopic confirmation of the galaxy counterpart of the intervening DLA at
z=3.096 in the field of GRB 070721B (z_GRB=3.6298) as proposed by other
authors. We also identify good candidates for the galaxy counterparts of the
two strong MgII absorbers at z=0.6915 and 1.4288 towards GRB 050820A
(z_GRB=2.615). The properties of the detected DLA galaxy are typical for
Lyman-break galaxies (LBGs) at similar redshifts; a young, highly starforming
galaxy that shows evidence for a galactic outflow. This supports the hypothesis
that a DLA can be the gaseous halo of an LBG. In addition, we report a redshift
coincidence of different objects associated with metal lines in the same field,
separated by 130-161 kpc. The high detection rate of three correlated
structures on a length scale as small as ~150 kpc in two pairs of lines of
sight is intriguing. The absorbers in each of these are most likely not part of
the same gravitationally bound structure. They more likely represent groups of
galaxies.
