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The interstellar medium of galaxies is filled with holes, bubbles, and shells, typically interpreted as remnants of stellar evolution. There is growing interest in the study of their properties to investigate stellar and supernova feedback. So far, the detection of cavities in observational and numerical data is mostly done visually and, hence, is prone to biases. Therefore, we present an automated, objective method for discovering cavities in particle simulations, with demonstrations using hydrodynamical simulations of a dwarf galaxy. The suggested technique extracts holes based on the persistent homology of particle positions and identifies tight boundary points around each. With a synthetic ground-truth analysis, we investigate the relationship between data density and the detection radius, demonstrating that higher data density also allows for the robust detection of smaller cavities. By tracking the boundary points, we can measure the shape and physical properties of the cavity, such as its temperature. In this contribution, we detect 808 holes in 21 simulation snapshots. We classified the holes into supernova-blown bubbles and cavities unrelated to stellar feedback activity based on their temperature profile and expansion behaviour during the 100 million years covered by the simulation snapshots analysed for this work. Surprisingly, less than 40% of the detected cavities can unequivocally be linked to stellar evolution. Moreover, about 36% of the cavities are contracting, while 59% are expanding. The rest do not change for a few million years. Clearly, it is erroneous to interpret observational data based on the premise that all cavities are supernova-related and expanding. This study reveals that supernova-driven bubbles typically exhibit smaller diameters, larger expansion velocities, and lower kinetic ages (with a maximum of 220 million years) compared to other cavities.