  The aim of this work is to investigate in a physical and quantitative way the
spectral evolution of bright Neutron Star Low-Mass X-ray Binaries (NS LMXBs),
with special regard to the transient hard X-ray tails. We analyzed INTEGRAL
data for five sources (GX 5-1, GX 349+2, GX 13+1, GX 3+1, GX 9+1) and built
broad-band X-ray spectra from JEM-X1 and IBIS/ISGRI data. For each source,
X-ray spectra from different states were fitted with the recently proposed
model compTB. The spectra have been fit with a two-compTB model. In all cases
the first compTB describes the dominant part of the spectrum that we interpret
as thermal Comptonization of soft seed photons (< 1 keV), likely from the
accretion disk, by a 3-5 keV corona. In all cases, this component does not
evolve much in terms of Comptonization efficiency, with the system converging
to thermal equilibrium for increasing accretion rate. The second compTB varies
more dramatically spanning from bulk plus thermal Comptonization of blackbody
seed photons to the blackbody emission alone. These seed photons (R < 12 km,
kT_s > 1 keV), likely from the neutron star and the innermost part of the
system, the Transition Layer, are Comptonized by matter in a converging flow.
The presence and nature of this second compTB component (be it a pure blackbody
or Comptonized) are related to the inner local accretion rate which can
influence the transient behaviour of the hard tail: high values of accretion
rates correspond to an efficient Bulk Comptonization process (bulk parameter
delta > 0) while even higher values of accretion rates suppress the
Comptonization, resulting in simple blackbody emission (delta=0).
