  By applying the dimensionless scheme, we investigate the quasinormal modes
and phase transitions analytically for three types of regular black holes. The
universal deviations to the first law of mechanics in regular black holes are
proved. Meanwhile, we verify that second order phase transitions and Davies
points still exist in these three models. In addition, we calculate their
quasinormal modes in the eikonal limit by applying the light ring/quasinormal
mode correspondence, and discuss the spiral-like shapes and the relations
between the quasinormal modes and phase transitions. As the main result, we
show that spiral-like shapes in the complex frequency plane are closely related
to the parameterization, namely in some particular units the spiral-like shapes
will emerge in the models, which may not be of the spiral behaviors reported by
other authors. We also discover a universal property of regular black holes,
i.e., the imaginary parts of their QNMs do not vanish for the extreme cases,
which does not appear in singular black holes, such as the Reissner-Nordstr\"om
and Kerr black holes, etc.
