The influence of various parameters characterizing the single- and double-pulse energy deposition (ED) upstream of a blunt body (distance between the deposition point and the body, amount of the energy and time delay between the pulses) on the topology of the supersonic flow at Mach 2 is studied experimentally and numerically. The obtained pressure-time diagram at the upstream stagnation point of the body as well as some significant topological properties of the bow-shock / heated-bubble interaction, like shock deformation and reflection, as well as the evolution of the heated bubble into the vortex ring downstream, are analyzed as resulting from the shock-decelerated spherical light-gas inhomogeneity. The evolution and topology of the interfering heated bubbles by double-pulse ED show the significance of vorticity generation initiated by blast-waves coming from the neighboring bubbles.