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We present an analysis of the spectral and timing properties observed in X-rays from Neutron Star (NS) X-ray binary GX3+1 during long-term transitions between the faint and bright phases of luminosity superimposed on short-term transitions between lower banana (LB) and upper banana (UB) branches in terms of its color–color diagram. We analyze all observations of this source obtained with the RXTE and BeppoSAX satellites. We find that the X-ray broad-band energy spectra during all these spectral transitions can be adequately reproduced by a composition of low-temperature blackbody component, a Comptonized component (COMPTB) and Gaussian line component. We argue that electron temperature kT_e of Compton cloud monotonically increased from 2.3 keV to 4.5 keV when GX3+1 makes a transition from UB to LB, related to low flux variabilities on time scale of hours. We also detect an evolution of noise components (a very low frequency noise and a high frequency noise) during these LB-UB transitions. Using the disk ``seed'' (COMPTB) normalization, which is proportional to the mass accretion rate, we found that the photon power-law index is almost constant (\Gamma=2.00+/-0.02) when mass accretion rate changes by factor four. We interpret this quasi-stability of the index \Gamma and a particular form of the spectrum in the framework of a model in which the energy release in the transition layer located between the accretion disk and NS surface dominates that in disk. Moreover, this index stability effect now established for GX3+1 was previously found in the atoll source 4U1728-34 and suggested for a number of other low mass X-ray neutron star binaries (see Farinelli & Titarchuk, 2011). This intrinsic behavior of NSs, in particular, for atoll sources, is fundamentally different from that seen in black hole binary sources where the index monotonically increases during spectral transition from the low state to the high state and then finally saturates at high values of mass accretion rate.