Cache-Control: private and
Cache-Control: max-age=0 and will automatically pass the object. To instruct Fastly to not cache
Cache-Control: no-cache and
Cache-Control: no-store you can create a Cache Setting (Under Settings/Cache Settings) with an action of Pass. Add a condition to the new rule so that it executes if the Cache-Control header exists. For example you would add the following condition to your new rule:
beresp.http.Cache-Control ~ "(no-cache|no-store)".