<p>This work investigates topological chaos for homeomorphisms of the open annulus, introducing a new set of sufficient conditions based on points with distinct rotation numbers and their topological relations to invariant continua. These conditions allow us to formulate classic methods for verifying annular chaos in a finitely verifiable version supported on basic properties of the map. The results pave the way for simple computer-assisted proofs of chaos in a wide range of annular maps, including many well–known examples, and we present these proofs for some analytic families, demonstrating the effectiveness of the method.</p>