To avoid repeating between, use both:
The interactions between both X and Y and X and Z are shown.
The reader will need to do a slight amount of parsing to understand this, but the use of both indicates that there are exactly two things being looked at. Since there are two things, the most reasonable parsing that can be made is (X and Y) and (X and Z).
If both is not used, then we don't know how many or which combinations are being described.
If X is a long phrase that you don't want to repeat, then turn it into two sentences and use a pronoun twice.
X is [something]. The interactions between both it and Y and it and Z are shown.
If you don't simplify it in this way, then the length of X will make any parsing of the combination of the two things too complicated for quick understanding.
Of course, if either Y or Z is also a long phrase, then it's likely you don't want to express it all in a single sentence anyway.
If that's the case, then use a horizontal or vertical list.
These two interactions are shown: (1) X and Y; (2) X and Z.
These two interactions are shown:
With lists like this, you could likely also repeat X in full without worrying about using a pronoun.