  We consider a two-dimensional, tangentially active, semi-flexible,
self-avoiding polymer to find a dynamical re-entrant transition between motile
open chains and spinning achiral spirals with increasing activity. Utilizing
probability distributions of the turning number, we ascertain the comparative
stability of the spiral structure and present a detailed phase diagram within
the activity inertia plane. The onset of spiral formation at low activity
levels is governed by a torque balance and is independent of inertia. At higher
activities, however, inertial effects lead to spiral destabilization, an effect
absent in the overdamped limit. We further delineate alterations in size and
shape by analyzing the end-to-end distance distribution and the radius of
gyration tensor. The Kullback-Leibler divergence from equilibrium distributions
exhibits a non-monotonic relationship with activity, reaching a peak at the
most compact spirals characterized by the most persistent spinning. As inertia
increases, this divergence from equilibrium diminishes.
