Quasi-reversible Creation-annihilation Models: Colliding Bullet Model with Creations and a Loop Model

We consider a large class of creation-annihilation models that contains, in particular, the colliding bullet model with creations and a loop model. For this large class of creation-annihilation models, we give sufficient conditions on their parameter to be rot(π)-quasi-reversible and to be rot(π/2)-quasi-reversible. Moreover, those conditions assure them that one of their stationary measures is described by a Poisson point process. These results, applied to the colliding bullet model with creations, are the first steps to study its non-empty stationary measure, and, applied to the loop model, prove its invariance according to all the symmetries of the square.