Legendary pokemon Connections the lake trio and Mew?

Mew and the lake trio have a lot of common, Trio and Mew: the four are of a single type, the Psychic-type, Uxie and Mew: knowledge (ability) Mew knows the move Transform it can transform all pokemon that have different abilities, Azelf and Mew: willpower (stats and moves) Mew knows all the moves, Mesprit and Mew: 2 Connections 1. emotions (nature and happiness) Mew has both of those, 2. both of the same Behavior Mew and Mesprit are both playfull. So what is the Connection beten them?