[zokier]

The animations turn these diagrams into hybrid between basic box-and-arrows diagrams and sequence diagrams, because the animations capture the temporal relationship between actions. They certainly can not be naively substituted with static arrows without loss of information.

[Veuxdo]

As noted below, the right tool for that is a sequence diagram [0]. These can be static images and read at one's own pace.

[0] https://en.wikipedia.org/wiki/Sequence_diagram