  The aim of this paper is to discuss the constructivity of the method
originally introduced by U. Bessi to approach the phenomenon of topological
instability commonly known as Arnold's Diffusion. By adapting results and
proofs from existing works and introducing additional tools where necessary, it
is shown how, at least for a (well known) paradigmatic model, it is possible to
obtain a rigorous proof on a suitable discrete space, which can be fully
implemented on a computer. A selection of explicitly constructed diffusing
trajectories for the system at hand is presented in the final section.
