Georgia, Armenia and Azerbaijan were all former parts of the Persian Empire, in a past that is remote enough not to sound threatening any longer. The three republics have been strongly influenced by Persian culture and its heritage is still visible and tangible in the art, language and architecture of the South Caucasus. This historic heritage has been preserved regardless of the twists and turns of international relations, and the fact that investments from and to Iran might be more easily accessible and more open could further enhance the exchange and the promotion of common assets. Something should be stressed here: this is an ongoing process, the ball is already rolling. Iran might have been an international pariah in other theaters, but it has never been left as an outsider in the South Caucasus. It preserved its regional relevance, and it kept developing its relations with the two plus one - Georgia does not actually share any border with Iran - northern neighbors.
For the three post-Soviet Republics trade exchange and diplomatic ties with Iran were till the very recent past to be molded not only consistently with the nature of the bilateral relation but, often on the tightrope, with the international commitments undertaken. Now things may go more smoothly, at least this is what can be assumed from a short review of what happened and what is happening in the last months in Georgia, Armenia and Azerbaijan. Necessarily singularly, one by one.
My commentary for AVIM: http://www.avim.org.tr/analiz/en/IRAN-AND-THE-SOUTH-CAUCASUS:-THE-IMPACT-OF-THE-NUCLEAR-DEAL-/4166