  We have systematically studied a large sample of the neutron star low mass
X-ray binaries (LMXBs) monitored by the Rossi X-ray Timing Explorer (50
sources; 10000+ observations). We find that the hysteresis patterns between
Compton dominated and thermal dominated states, typically observed in black
hole LMXBs, are also common in neutron star systems. These patterns, which also
sample intermediate states, are found when looking at the evolution of both
X-ray colour and fast variability of ten systems accreting below ~ 30 % of the
Eddington Luminosity. We show that hysteresis does not require large changes in
luminosity and it is the natural form that state transitions take at these
luminosities. At higher accretion rates neutron stars do not show hysteresis,
and they remain in a thermal dominated, low variability state, characterized by
flaring behaviour and fast colour changes. Only at luminosities close to the
Eddington Luminosity, are high variability levels seen again, in correspondence
to an increase in the fractional contribution of the Comptonization component.
We compare this behaviour with that observed in LMXBs harbouring black holes,
showing that the spectral, timing and multi-wavelength properties of a given
source can be determined by its location in the fast variability-luminosity
diagram, which, therefore, provides a common framework for neutron star and
black hole accretion states.
