Originality: This paper introduces for the first time an operational theory of interaction nets: in particular techniques and tools to compute when two programs are equivalent. Rigour: The main result of the paper, that contextual equivalence and bisimilarity coincide, gives a powerful proof technique that has been used to prove correct compiler optimisations, and correctness proofs of encodings of other languages into interaction nets. Significance: Brings powerful operational techniques into the realm of interaction nets. Impact: This work has been used as the starting point for several other studies of operational equivalence, including two PhD theses at other institutions.