An "imaginary transition structure" overlays the molecular graphs of the educt and product sides of an elementary chemical reaction in a single graph to highlight the changes in bond structure. We generalize this idea to reactions with complex mechanisms in a formally rigorous approach based on composing arrow-pushing steps represented as graph-transformation rules to construct an overall composite rule and a derived transition structure. This transition structure retains information about transient bond changes that are invisible at the overall level and can be constructed automatically from an existing database of detailed enzymatic mechanisms. We use the construction to (i) illuminate the distribution of catalytic action across enzymes and substrates and (ii) to search in a large database for reactions of known or unknown mechanisms that are compatible with the mechanism captured by the constructed composite rule.