  We present a rotating regular black hole whose inner horizon has zero surface
gravity for any value of the spin parameter, and is therefore stable against
mass inflation. Our metric is built by combining two successful strategies for
regularizing singularities, i.e. by replacing the mass parameter with a
function of $r$ and by introducing a conformal factor. The mass function
controls the properties of the inner horizon, whose displacement away from the
Kerr geometry's inner horizon is quantified in terms of a parameter $e$; while
the conformal factor regularizes the singularity in a way that is parametrized
by the dimensionful quantity $b$. The resulting line element not only avoids
the stability issues that are common to regular black hole models endowed with
inner horizons, but is also free of problematic properties of the Kerr
geometry, such as the existence of closed timelike curves. While the proposed
metric has all the phenomenological relevant features of singular rotating
black holes -- such as ergospheres, light ring and innermost stable circular
orbit -- showing a remarkable similarity to a Kerr black hole in its exterior,
it allows nonetheless sizable deviations, especially for large values of the
spin parameter $a$. In this sense, the proposed rotating "inner-degenarate"
regular black hole solution is not only amenable to further theoretical
investigations but most of all can represent a viable geometry to contrast to
the Kerr one in future phenomenological tests.
