The sequence of the electronic flow driving the hydrometallation of acetylene by lithium hydride (and that of the opposite beta-hydride elimination reaction from the alkenyl metal intermediate), was examined within the perspective provided by the bonding evolution theory (BET). The analysis was based on the application of catastrophe theory to the changes of the electron localization function topology along the intrinsic reaction coordinate. The description of the electronic processes occurring on the process was represented in terms of topological structural stability domains (SSDs) and the associated elementary bifurcation catastrophes. Within such a framework of representation, the "evolution" of the system through the different SSDs reveals the key chemical events driving the transformation, including the large polarization effect as a consequence of Pauli repulsion between ions of the positive cationic metal on the hydride domain, the activation of the CC triple bond to attack the cationic center, and the agostic stabilizing interactions involving the hardest cationic metal, followed by the attack of the hydride center. These results contribute to emphasizing the intrinsic value and usefulness of using topological-based approaches and associated tools to increase our knowledge and understanding of the subtleties underlying the electronic flow as nuclei evolve along the reaction coordinate, providing detailed and complementary insights in comparison to other interpretative tool such those based on orbital-based representations, concerning the intimate nature of the electronic rearrangement of key mechanistic processes in chemistry.