We define ∆-equivalence for operator systems and show that it is identical to stable isomorphism. We define ∆-contexts and bihomomorphism contexts and show that two operator systems are ∆-equivalent if and only if they can be placed in a ∆-context, equivalently, in a bihomomorphism context. We show that nuclearity for a variety of tensor products is an invariant for ∆-equivalence and that function systems are ∆-equivalent precisely when they are order isomorphic. We prove that ∆-equivalent operator systems have equivalent categories of representations. As an application, we characterise ∆-equivalence of graph operator systems in combinatorial terms.