Are any of the games canon to one another or are they multiverse type deals? (minor endgame spoilers for Mother 3)

I ask this question because apparently I found out earlier that Porky is the same Porky from Mother 2 and somehow used a Time distortion device to come to Lucas' world. Therefore this can only mean that all the games are in their own world. However, Mother 1 & 2 seem to be linked as Giygas is the final boss in both games.