You can only trade crafted pinks that were dropped from campaigns. Mystery and I guess cyber are exceptions because they are obtained from quests, so they cannot be traded. Generally, a crafted item changes stats from its previous form and takes on a new name. For example, the Mega Mage set from sewers turns into Enchanted when you craft it in the town. It's sort of hard to explain because crafting items is kind of inconsistent from campaign to campaign, but there are threads in the traders market that has a list of all the crafted sets from Sewers-BSM/Ancient Caverns.

Also, just note how crafting items started at sewers, the campaigns before that did not have the option to craft sets.