Persistence diagrams are one of the main tools in field Topological Data Analysis (TDA). They contain fruitful information about shape data. The use machine learning algorithms on space persistence proves to be challenging as lacks an inner product. For that reason, transforming these a way is compatible with important topic currently researched TDA. In this paper, our contribution consists thr...

The purpose of this note is to describe a new set of numerical invariants, the relevant level persistence numbers, and make explicit their relationship with the four types of bar codes, a more familiar set of complete invariants for level persistence. The paper provides the opportunity to compare level persistence with the persistence introduced by EdelsbrunnerLetscher-Zomorodian called in this...