persist (action)
to continue to do or say something in a determined way
‘But why?’ he persisted.
persist in: She persisted in her refusal to pay.
persist in doing something: Why do you persist in denying that it was your fault?
insist (idea, belief, viewpoint)
1. to say very firmly that something must happen or must be done
You must see a doctor immediately – I insist.
insist (that): She insisted that we stay at her house instead of a hotel.
insist on: Some companies insist on staff undergoing regular medical checks.
2. to keep saying very firmly that something is true, even when other people will not believe you
insist (that): The school insists that it is doing everything it can to cooperate.
insist on: He has insisted on his innocence from the beginning.
stick to (plan, promise, belief)
[stick to something] to do something that you promised or decided you would do, or that you believe you should do
We said we’d give her the cash, and we must stick to our agreement.