Does anyone know any source containing an example of persistent homology being explicitly, manually calculated? That is, as opposed to being calculated on by computer.
I am just looking for a simple example with a few simplices that can be worked out by hand for learning purposes.
In Computational Topology an Introduction by Edelsbrunner and Harer they manually compute the reduced persistent homology of a $2$-simplex. They use reduced homology to give it some level of interest.