ERASED (2016)

12 episodes. A struggling manga artist with a habit of slipping back a few minutes in time is suddenly sent back 18 years to 1988, with a chance to prevent a classmate's disappearance before it happens. The best gateway on this list for anyone who wants a gripping mystery first and anime second. Nearly every episode ends on a hook that makes stopping hard, and the childhood friendships give the time-travel premise real warmth. The anime wraps up its story differently from the manga, so readers of the original should expect a changed final stretch.