The past and the future are obviously rather different in some ways, as everyone knows [one has happened already and the other has not] but I very much agree with you when you say that the "process" of past and future are in essence the same in our minds. Indeed, in the last few years I have written and given talks on the very theme, and have coined a new word. "chronesthesia," to refer to the kind of brain/mind capacity, or consciousness, that MAKES IT POSSIBLE for humans to mentally travel in time, into their own past and into their own future.
If you go to Google and use the key words "tulving, chronesthesia" you find out a bit more. Read especially a short report of a talk I gave at the APA (American Psychological Association) meeting in 2003. But the whole idea is rather new in cognitive neuroscience and therefore there has not been much actual empirical research on it, yet.