Abstract: It is classically known that two lens spaces L(p,q) and L(p,q') and their products with S^2 are diffeomorphic if and only if q'\equiv \pm q^{-\pm 1} in mod p. The non-trivial part of this statement is established via the Reidemeister torsion. In this talk, we explore the possibility of capturing the above relation using holomorphic curves in the symplectizations. We endow lens spaces with the contact form that is the quotient of the standard contact form on S^3 and in the case of unit cotangent bundles, the contact form is the quotient of the contact form on the unit cotangent bundle of S^3 induced by the round metric. In both cases, the moduli spaces of curves with at most two non-contractible ends are easy to be described. Using these moduli spaces in a neck-stretching procedure, we aim to show that given a contactomorphism between two lens spaces or two unit cotangent bundles, the above relation is fulfilled. It turns out that, this is not possible using the standard methods, which is expected because of the theoretical background of the problem. After pointing out what goes wrong along the procedure, we show that imposing conditions on the contactatomorphism solves both the technical and essential issues of the procedure. In the case of unit cotangent bundles, the conditions we impose are global bounds on the contactomorphism, while in the case of lens spaces, the condition is the strictness along a single contractible orbit.