Interacting galaxies are galaxies sufficiently close in space that their mutual gravity distorts their structure. Usually interacting galaxies are gravitationally bound, but "it ain't necessarily so."

There are 4 simple characteristics that mark interacting galaxies:

Distorted or warped galaxy disks. A non-interacting spiral galaxy has a very flat galaxy disk.
There are connecting bridges (Cimatti-163) of stars and maybe interstellar medium (ISM) between the galaxies. The stars are NOT usually resolved, of course, and so the bridges are just diffuse glowing bridges.
The galaxies have tidal tails: long streams of stars stretching away from the galaxies.
The galaxies have a separation in space comparable to their size scale or less. In this case, they are probably interacting gravitationally even if there are no other signs. Unfortunately, it is hard to tell if galaxies close in angular separation are close in space. However, if a pair of galaxies are very close in angular separation and about the same in angular size, then that is two improbabilities, unless the galaxies are close in space where they shared similar evolution. Improbable things do happen, and so this argument is weak for the galaxies being interacting galaxies.
Note if galaxies are close in angular separation, but so different in angular size scale that they look like they must far apart in space, they are probably NOT interacting, unless other evidence shows that they probably are. This is also a weak argument since galaxies can have very different spatial scales, and so can look far apart in space when they are NOT.

Of course, some interacting galaxies may have none of these characteristics in any obvious way. It is hard to tell in some cases if galaxies are interacting galaxies.