Topology offers a practical set of computational tools to accurately predict certain physical and chemical properties of materials including transformations under deformation. In network glasses with increased cross-linking three generic elastic phases are observed. We examine ternary GexSbxSe100-2x glasses in Raman scattering, modulated DSC and volumetric measurements, and observe the rigidity transition, x = x(c)(1) = 14.9% that separates the flexible phase from the Intermediate phase, and the stress transition, x = x(c)(2) = 17.5% that separate the intermediate phase from the stressed rigid one. Raman scattering provides evidence of the structural motifs populated in these networks. Using size increasing cluster agglomeration, we have calculated the rigidity and stress transitions to occur near x(c)(1)(t) = 15.2% and x(c)(2)(t) = 17.5%, respectively. Theory predicts and experiments confirm that these two transitions will coalesce if edge-sharing Ge-tetrahedral motifs were absent in the structure, a circumstance that prevails in the Ge-deficient Ge7SbxSe93-x ternary, underscoring the central role played by topology in network glasses. We have constructed a global elastic phase diagram of the Ge-Sb-Se ternary that provides a roadmap to network functionality. In this diagram, regions labeled A, B, and C comprise networks that are flexible, rigid but unstressed, and stressed-rigid, respectively.