This paper addresses the problem of verifying equivalence between a pair of programs that operate over databases with different schemas. This problem is particularly important in the context of web applications, which typically undergo database refactoring either for performance or maintainability reasons. While the web application should have the same externally observable behavior before and after schema migration, there are no existing tools for proving equivalence of such programs. This paper takes a first step towards solving this problem by formalizing the equivalence and refinement checking problems for database-driven applications. We then propose a proof methodology based on the notion of bisimulation invariants over a new logic called the theory of relational algebra with updates. We also present a fully automated technique for synthesizing such bisimulation invariants and automatically verify their correctness. We have implemented the proposed technique in a tool called Mediator and show that it can verify the equivalence of real-world web applications containing hundreds of transactions.