  We construct traversable thin-shell wormholes which are asymptotically Ads/dS
applying the cut and paste procedure for the case of an acoustic metric created
by a relativistic Bose-Einstein condensate. We examine several definitions of
the flare-out condition along with the violation or not of the energy
conditions for such relativistic geometries. Under reasonable assumptions about
the equation of state of the matter located at the shell, we concentrate on the
mechanical stability of wormholes under radial perturbation preserving the
original spherical symmetry. To do so, we consider linearized perturbations
around static solutions. We obtain that dS acoustic wormholes remain stable
under radial perturbations as long as they have small radius, such wormholes
with finite radius do not violate the strong/null energy condition. Besides, we
show that stable Ads wormhole satisfy some of the energy conditions whereas
unstable Ads wormhole with large radii violate them.
