The Beginning
Renton comes face-to-face with Anemone, the girl he met in his dreams, after returning from the Corallian Zone. Both Anemone and Eureka appear to be having intense headaches, making it seem as if the same thing is affecting them. So, Dominic and Renton go into the city to find medicine for them.
Aired 10/07/2005EP 13 - The Beginning

Eureka Seven
Renton is a teenager trapped working as a mechanic in a backwater town. He dreams of joining up with a daredevil group of pilots known as Gekkostate and following in his father's heroic footsteps.
When a mysterious beauty named Eureka shows up asking for a tune-up, Renton soon finds himself drawn into a high-flying mecha dogfight that makes him a target of the military. When the dust settles on the spectacular battle, Renton is invited to join Gekkostate, but he soon discovers that even a dream come true has a dark side.
(Source: Funimation)