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We add mobility to Place-Transition Petri Nets: tokens are names for places, and an input-token of a transition can be used in its postset to specify a destination. Mobile Petri Nets are then further extended to Dynamic Nets, by adding the possibility of creating new nets during the firing of a transition. In this way, starting form Petri Nets, we define a simple hierarchy of Nets with increasing degrees of dinamicity. For each class in this hierarchy we provide its encoding in the former class. Our work has been largely inspired by the join-calculus of Fournet and Gonthier, that turns to be a (well motivated) particular case of Dynamic Petri Nets. The main difference is that, in the preset of a transition, we allow both non-linear patterns (name unification) and (locally) free names for input places (i.e. we remove the locality constraints, and preserve reflexion).