The basic setting for topological transformation is double simple-deform modifier.
Also, register empty to axis, origin of simple deform modifier.
To transform object, tweak angle in the modifier, and change location/rotation/scale of an empty.
Showcase of transformation with monkey:
I think the transformation by double simple-deform modifier makes a sense of totem in traditional societies.
The transformation below is my favorite shape in the series. It’s like an elder owl.