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is it variety and to tie one paragraph to another
I'm not so sure about variety, but it's definitely to tie them together.
Coherence can be seen as a sort of tie between the big picture.
Variety just means that there are differences
and that leaves you with tying one paragraph to the next. Simply, if you wanted to tie the entire thing together, you would just read a two-sentence spoiler or something. Transition sentences are used to move from one paragraph to another in order to provide smoothness.
Without them, it's kind of like "Where did this even come from?"
So, its coherence and to tie one paragraph to another.