  The recent opening of gravitational wave astronomy has shifted the debate
about black hole mimickers from a purely theoretical arena to a
phenomenological one. In this respect, missing a definitive quantum gravity
theory, the possibility to have simple, meta-geometries describing in a compact
way alternative phenomenologically viable scenarios is potentially very
appealing. A recently proposed metric by Simpson and Visser is exactly an
example of such meta-geometry describing, for different values of a single
parameter, different non-rotating black hole mimickers. Here, we employ the
Newman--Janis procedure to construct a rotating generalisation of such
geometry. We obtain a stationary, axially symmetric metric that depends on
mass, spin and an additional real parameter $\ell$. According to the value of
such parameter, the metric may represent a rotating traversable wormhole, a
rotating regular black hole with one or two horizons, or three more limiting
cases. By studying the internal and external rich structure of such solutions,
we show that the obtained metric describes a family of interesting and simple
regular geometries providing viable Kerr black hole mimickers for future
phenomenological studies.
