Observation of the Reversibility windows (RWs) in binary Ge_xS_100‐x, As_xS_100‐x and ternary Ge_xAs_xS_100‐2x glass systems has permitted constructing a global Topological Phase diagram in the Ge‐As‐S composition triangle. The RW denotes glass compositions for which the Enthalpy of relaxation at T_g becomes vanishing, leading to thermally reversing glass transitions. The phase diagram permits delineating glass compositions that are in the Flexible phase (FP), Intermediate Phase (IP) and the Stressed‐Rigid Phase (SRP) for all ternary Ge_xAs_xS_100‐2x glass compositions. For the IP compositions examined, we also observe a general lowering of the molar volumes, V_m, in relation to those for non‐IP compositions, giving rise to a Volumetric window. Melt dynamics of IP‐compositions reveal a fragility index, m < 20, lower than for non‐IP melts for which m > 20 displaying a Fragility window, underscoring in part the reason for delayed homogenization of melts in these sulfide glasses. The observation of the three types of Windows characteristic of IP compositions, became feasible only once homogeneous bulk glasses are synthesized, in which the variance, <Δx> in As and Ge concentration, x, across batch compositions is less than 0.01%. This was established by Fourier Transform – Raman (FT‐Raman) profiling each batch composition synthesized.