  [Abridged] We characterise a massive proto-cluster at z=2.895 that we found
in the COSMOS field using the spectroscopic sample of the VIMOS Ultra-Deep
Survey (VUDS). This is one of the rare structures at z~3 not identified around
AGNs or radio galaxies, so it is an ideal laboratory to study galaxy formation
in dense environments. The structure comprises 12 galaxies with secure
spectroscopic redshift in an area of 7'x8', in a z bin of Dz=0.016. The
measured galaxy number overdensity is delta_g=12+/-2. This overdensity has
total mass of M~8.1x10^(14)M_sun in a volume of 13x15x17 Mpc^3. Simulations
indicate that such an overdensity at z~2.9 is a proto-cluster that will
collapse in a cluster of total mass M~2.5x10^(15)M_sun at z=0. We compare the
properties of the galaxies within the overdensity with a control sample at the
same z but outside the overdensity. We did not find any statistically
significant difference between the properties (stellar mass, SFR, sSFR, NUV-r,
r-K) of the galaxies inside and outside the overdensity. The stacked spectrum
of galaxies in the overdensity background shows a significant absorption
feature at the wavelength of Lya redshifted at z=2.895 (lambda=4736 A), with a
rest frame EW = 4+/- 1.4 A. Stacking only background galaxies without
intervening sources at z~2.9 along their line of sight, we find that this
absorption feature has a rest frame EW of 10.8+/-3.7 A, with a detection S/N of
~4. These EW values imply a high column density (N(HI)~3-20x10^(19)cm^(-2)),
consistent with a scenario where such absorption is due to intervening cold gas
streams, falling into the halo potential wells of the proto-cluster galaxies.
However, we cannot exclude the hypothesis that this absorption is due to the
diffuse gas within the overdensity.
