The fact that light carries orbital angular momentum (OAM) associated to singularities embedded in the phase function of optical fields was recently discovered by Allen. A couple of years later, Courtial demonstrated that light beams might also possess OAM without the presence of a singularity. Over the past years, OAM has been the subject of intense experimental and theoretical study, including its conservation. Laguerre-Gaussian and Bessel are among the most well-known beams with phase singularities carrying OAM. Fairly recently, Dholakia et al. generated, by inserting a phase singularity into the main lobe of an Airy beam, a novel kind of beam carrying OAM. As was expected, the vortex accelerates in a direction perpendicular to the beam axis of propagation similar to an Airy beam. Motívate by this peculiarity, we experimentally generated two Airy-vortex beams with opposite acceleration in order to study the OAM during the collision. To our knowledge, there are no reports on the analysis of OAM in collisions of beams carrying OAM. Two experiments were carried out, the first one involves collisions of two beams carrying the same amount of OAM. In the second one, we collide beams carrying opposite OAM. Analysis of the phase function from several planes perpendicular to the propagation axis leads us to conclude that after the collision of two beams having the same OAM, the phase singularity does not disappear. Whereas in the case where the beams have opposite OAM, the phase singularity annihilates during the collision. These experiences suggest a conservation of the OAM associated with phase singularities. Analysis of the phase was done by means of a new technique proposed by Mazilu et al., which allows to detect and track the singularities embedded in the phase function.