Here is how you can answer the question. Get a hold of a Moss Motors or The Roadster Factory catalog and look up the top in question. Especially the Moss catalog does a great job defining what top fits what car. In this case it will show that the top fits certain TR2 cars through TR3 up to a commission number . There is also a note in the catalog about the "baby tenax" used in some TR2's that are no longer available, thus requiring you to change over to the "standard Tenax" . It sounds like this conversion will have to be done eventually if you get a new top later anyway. But do check this source (likely you can do it online if you do not have a catalog) to verify what your car is and what (hopefully you know the commission number of the TR3 that the top came off of)the top you speak of fits.
Another way to find this information out is to get a spare parts catalog ( which you must buy) for each of the TR2 and TR3 and check out the actual part numbers. But this may still not give you a good answer as it will only indicate that there was a change and not what the change was.
Hope that this helps to lead you in the direction to better understand what your car is in relation to the cars that came later.
This is especially important when doing a restoration and looking for used parts.
Best of luck.
Charley Fitch
Maintenance Issues
