Among the formalisms that can be used to reason about concurrent systems, process calculi stand out both for their simple syntax and close connection to reversibility. They also offer approaches to study relations such as dependence, concurrency or causality between transitions, useful in exploring e.g., causes of bugs or how to multi-thread executions. This paper offers two main contributions: first, we provide separate definitions of a dependence relation and an independence relation, and prove their complementarity on connected transitions instead of postulating it, as is usually done. We also prove that those relations, as well as the notions of event, concurrency, causality and conflict, are unique for any reversible system respecting basic sanity axioms. Second, we prove that the operational definitions of core independence and causality coincide with their characterisations using a pre-existing syntactic mechanism in reversible process calculi, namely communication keys.