Each email click and open gets tracked in ESP. For example - if a user clicks on the same link twice, it will count as 2 clicks in the total number of clicks for this email campaign.
If a user opens the email twice, this will usually count as 2 opens as well in most cases. The calculation is slightly less accurate for opens because the tracking for this is implemented in such a way, that we record events of invisible pixels loading. These are by default included in the template of any newsletter campaign. Therefore it is up to the email services (like Outlook, Thunderbird, Gmail, etc.) if they request the same pixel 3 times in succession or if they do it just once and then cache it for some time without making repeated requests.
On our side, of course, all required caching hints/headers are set to no-cache. So each individual event gets tracked (with some possibility for opens to behave slightly different, which is out of our control).