Learn how to detect topological changes that occur in dynamic 2D Delaunay triangulations using CUDA. We'll present a novel, unified approach that can be applied in all those cases (pedestrian tracking, flocking, moving bubbles, etc.) where objects are triangulated starting from a density map. Topological changes are detected comparing two subsequent triangulations and they show up as "flipped-edges." We'll show new physics results due to the unprecedented statistics of detection of irreversible topological changes, occurring in the triangulation of the droplets of a Lattice Boltzmann emulsion, allowed by our implementation. Such changes are associated to the so-called plastic events that are responsible for the complex behavior of emulsions possessing both liquid and solid features at the same time. In our implementation, we used a suitable mix of in-house developed CUDA kernels and primitives from existing CUDA libraries.