Are prior, previous, and preceding interchangeable?

Since you can't access OED, I'm quoting the definitions:

prior

• Existing or coming before in time, order, or importance:

previous:

• Existing or occurring before in time or order:

precede:

• Come before (something) in time:

• Come before in order or position:

None of them unambiguously preclude A, in my opinion.

You need more words. You should say something like:

"Moment D is the same as the two moments immediately preceding it"

For what it's worth, I agree with Tushar Raj on the need for 'immediately' to remove all ambiguity, even if the OED didn't help.

I often find that when I have a feeling about a word having meaning a shade different than its supposedly interchangeable synonyms, it usually comes from its etymological roots. While it's still not concretely definitive, Etymology Online can help. In this case, I think this may inform the subconscious coloring of meanings.

• Precede (Mid-French, Latin; ~1400s): the 'cede' root means "walk," as in, to walk before.
• Previous (Latin; ~1600s): the 'vious' root comes from 'via,' meaning "road."
• Prior (Old Latin, via Late Old English; 1714--but this is misleading, as it's likely older than the other two terms): the root is 'prae,' but includes not only "former, previous" like the others, but also "first, superior, and [fore]father."

So, maybe in this light, 'precede' implies an animate or active thing that came before; 'previous,' perhaps suggests something more relative between the two in time, space, or similar; and then 'prior,' not just a thing before, but greater in rank or at least that it broke ground or led the way substantially.

My understanding has been since 5th grade that preceding refers to an event occurring immediately before the one to which it is being compared, but that prior refers to a time that occurred before the one being referenced, while previous refers to an event that occurred before the one being referenced.

This understanding was reiterated in high school in debate class. The teachers I had in each of those two grades were sticklers for precise usage.