The potential energy surfaces (PES) for the interaction of Mn+ (S-7, S-5) with H2O, NH3, and CH4 have been studied within the framework provided by the electron localization function (ELF) analysis. This has been achieved by analyzing density functional theory calculations (B3LYP approach) using the bonding evolution theory. The main characteristic of the studied reactions is the involvement of more than a single spin surface in the reaction pathways, which means that a spin crossover occurs along the reaction coordinate. This type of reactions are usually classified in terms of the two-state reactivity (TSR) paradigm. The different domains of structural stability occurring along the reaction path have been identified as well as the bifurcation catastrophes responsible for the changes in the topology of the systems. The analysis provides a chemical description of the reaction mechanism in terms of agostic bond formation and breaking.