How to compare two shapes with the same geometry

Hi,

I looked up a lot of information and didn't find it. Here's my idea

1. compare whether the basic characteristics are the same, such as the number of internal Vertex, edges, faces, surface area, volume, moment of inertia around the main axis, etc

2. Compare topology data again
By reading the development documents, there are similar functions in 《shape healing》 documents. The original shape will be reorganized or modified, and the geometry before and after modification is the same. I wonder if you experts can give some suggestions.

Thanks in advance