If not listed, then the two regions are neutral/have no contact that’s notable.
Kanto + Johto = Same region. Lugia and Ho-Oh both rule over Kanto until Ho-Oh leaves. Lugia “continues” his reign but passes the reigns over to the Legendary Birds once they complete their training.
Kanto + Kalos = The Legendary Birds were tasked with helping Xerneas and Yveltal keep order in Kalos soon after they are revived (because Arceus thought the two needed some help post-slumber). They regularly patrolled and as a result are very familiar with the land. Yveltal has a good relationship with them, enough to call them his own apprentices at times, though Xerneas could care less about foreigners.
Johto + Hoenn = People from Hoenn travelled to Johto enough for the Embedded Tower to be created and for Rayquaza to have his own perch. Ho-Oh and Lugia were given Hoenn’s Naval Rock as a gift, as the both of them had a wonderful friendship with Rayquaza. After Ho-Oh leaves the relationship deteriorates until it becomes non-existant. Hoenn and Johto are very bitter towards each other as of now.
Johto + Sinnoh = A good relationship, but not as friendly as the one with Hoenn. Arceus first came across Ho-Oh and Lugia at the Sinjoh Ruins, which acts as a temple for both gods. Because Arceus is fascinated with the Unown he takes a great liking to both Lugia and Ho-Oh, and they become his right hands in the council. This relationship was not impacted by Ho-Oh’s departure.
Johto + Alola = Both Ho-Oh and Lugia fought against Necrozma to save the Cosmog which would eventually become Lunala and Solgaleo. The two celestial deities were in debt to the actions taken by the Tower Duo, so while they outcast and discriminate against almost every other region, they always check in with Lugia and maintain their happy alliance. Their relationship was only strengthened by Ho-Oh’s departure, and they regularly check in on Lugia to make sure he takes care of himself.
Hoenn + Sinnoh = Rayquaza and Arceus have an almost “best friend” relationship because Rayquaza was one of the first legends not created by Arceus that the original one encountered. Regigigas ultimately chose to rest in Sinnoh, not Hoenn, and their workings to bring the regions together and shape the world have made both countries almost inseparable.
Hoenn + Kalos = Rayquaza has tabs on Xerneas and Yveltal because they are the only one with knowledge on his condition. Rayquaza doesn’t so much visit as he does question about the Mega Evolution epidemic and how to stop it.
Unova = No one really likes or associates with Unova. Reshiram and Zekrom bite at anyone that tries to build a relationship with them and hate foreigners, so no other legend attempts to make an alliance. (Arceus doesn’t like them much but he’d never say it.)
Alola = Not many friends. Because of their experience as children Queen Lunala (Mizuki) and King Solgaleo (Hazuko) don’t make alliances and cut off all communications with the exception of Johto and occasionally Hoenn. They only return to inform Arceus that they have heirs, and then immediately leave.
Unown Universe + Johto = The Unown love Johto, and claim it as their own. In fact, every legend in Johto has Unown power in their blood- none are naturally born or made from Arceus. Ho-Oh ends up in the Unown’s universe after he nearly dies from his injuries. Some say it was because his soul was being reaped and his physical form got stuck as a result. Others say Necrozma had something to do with it because Ho-Oh was one of the only legends to fight him upfront and as a result he would hold a grudge.
Unown Universe + Sinnoh = The Unown aren’t very fond of Arceus, but do his bidding because he’s the only legend that can oppose them. They do their best to hide from Arceus especially after the Brass Tower burns.
Ultra Beasts Universe + Everyone = The Ultra Beasts will do anything to destroy the regions. They have no friends (though Celesteela has an unsettling fascination with Celebi) and are only subservient to Necrozma because he promised them power if they removed Solgaleo and Lunala from the picture. They can’t understand most legends and have a diet mainly based on Unown, automatically making them enemies with the Johto legends.