Several different notions of equivalence have been proposed for logic programs with answer set semantics, most notably strong equivalence. However, strong equivalence is not preserved by certain logic program operators such as the strong and weak forgetting operators of Zhang and Foo. We propose a stronger notion of equivalence, called T-equivalence, which is preserved by these operators. We give a syntactic definition and provide a model-theoretic characterisation of T-equivalence. We show that strong and weak forgetting does preserve T-equivalence and using this, arrive at a model-theoretic definition of the strong and weak forgetting operators.