The problem of achieving high performance from induction motor based drives - without sensing mechanical variables, i.e. high performance sensorless control - is a widely studied topic, specially in the last decade. Several works point out some operating regimes where reliable control and speed estimation fail. However, a complete understanding of the nature of these limitations does not exist due to the lack of a formal analysis of the observability properties of this kind of machines. In this paper a strategy is proposed to make a global analysis of the observability properties of the induction motor under sensorless conditions. The work aims at providing a formal answer to the fundamental question about the existence of indistinguishable internal trajectories for that electric machine. It is shown that there exist diverging trajectories corresponding to the same input-output behavior of the system, i.e. they are indistinguishable from the external signals. This implies the impossibility of constructing an observer that converges for every trajectory of the motor. This indistinguishable trajectories are input dependent, and the system cannot be decomposed into an observable and a non observable part. We give a complete characterization of the set of all indistinguishable trajectories, what we call indistinguishable dynamics. This description is valid for every value of the parameters.