Dimension Rush 1: Chaser's Paradise
A man had destroyed his own dimension by his own greed, now he has to travel across other dimensions to find ingredients that is able to revert back his dimension to where he left off.
He goes across various dimensions and meets many unique people, but the clocks ticking, because other people from dimensions don't really think he's welcomed here.
Dimension portals are mentioned throughout the story, they look like the thing from the cover, all the portal have different colours but the same structure.