Mahou no Yousei Persia: Escape!

Hatsuki is a highschool student living with her sister, Hatsumi, who she has a huge crush on. On Hatsumi's 16th birthday, she is suddenly surrounded by a green light and disappears in front of Hatsuki. She manages to follow Hatsumi with the help of a being resembling a fat baby chick (literally), ending up in a place called "The Great Library", which is full of different worlds stored in books. Hatsumi wasn't there, though, so the search for Hatsuki's great love begins and involves traveling from book to book. (Source: AniDB)

Cheng Ke has lost everything. Coming from a privileged background, he now has to search through trash to find his missing possessions. When one of his frustrated outbursts results in him being punched in the face, Cheng Ke finds himself unfortunately acquainted with terrifying gang leader Jiang Yuduo. Circumstances lead to Cheng Ke becoming a tenant at a new apartment—which just so happens to be rented out by Jiang Yuduo. Cheng Ke's inability to complete even the most menial tasks forces him to overly depend on his landlord, and as a result, the two form an indescribable bond. However, there are darker forces at play in the lives of both Cheng Ke and Jiang Yuduo. The two men are haunted by the pasts they left behind, and meanwhile, danger lurks around every corner. With mysterious figures following their every move, gang wars raging in the streets they walk on, and enemies itching to bring them down, Cheng Ke and Jiang Yuduo must always have each other's back. [Written by MAL Rewrite]

The OVA, bundled with the special edition version of the seventh manga volume, will tell an "other side" story centered on Mafuyu Satou and Ritsuka Uenoyama that wasn't featured in the Given movie. (Source: MAL News)

In the wake of a third world war which left Japan in ruins, an organization known as Vischio seized control of Tokyo and renamed it Toshima. Taking place in its back alleys are battle games known as Igura, overseen by the Vischio, in which contestants battle and bathe in each other's blood to earn the chance to go up against its tournament's king, Il-re. Igura is not the only fighting tournament around; Bl@ster is a similar yet vastly different game since it prohibits murder and the use of weapons. The only way to win is by knocking out the opponent. Akira, a young man isolated from his family, is known to be undefeatable at Bl@ster. However, his life on the top is shattered when he is accused of murder. Unable to prove his own innocence, all hope is seemingly lost... that is until a mysterious woman named Emma appears and offers him a chance. Now, to regain his freedom, Akira must participate in Igura and ultimately defeat Il-re. [Written by MAL Rewrite]