The OVA episode looks at the primary matches between the two schools and even includes interviews with the players 

A chance event triggered Shouyou Hinata's love for volleyball. His club had no members, but somehow persevered and finally made it into its very first and final regular match of middle school, where it was steamrolled by Tobio Kageyama, a superstar player known as "King of the Court." Vowing revenge, Hinata applied to the Karasuno High School volleyball club...only to come face-to-face with his hated rival, Kageyama! A tale of hot-blooded youth and volleyball from the pen of Haruichi Furudate!! 
(Source: Shonen Jump) 
Notes: 
- Winner of the 61st Shogakukan Manga Award in the Shounen Category in 2017. 
- Chapter count includes 2 extra chapters.

Following their participation at the Inter-High, the Karasuno High School volleyball team attempts to refocus their efforts, aiming to conquer the Spring tournament instead.
 
When they receive an invitation from long-standing rival Nekoma High, Karasuno agrees to take part in a large training camp alongside many notable volleyball teams in Tokyo and even some national level players. By playing with some of the toughest teams in Japan, they hope not only to sharpen their skills, but also come up with new attacks that would strengthen them. Moreover, Hinata and Kageyama attempt to devise a more powerful weapon, one that could possibly break the sturdiest of blocks.
 
Facing what may be their last chance at victory before the senior players graduate, the members of Karasuno's volleyball team must learn to settle their differences and train harder than ever if they hope to overcome formidable opponents old and new—including their archrival Aoba Jousai and its world-class setter Tooru Oikawa.
 
[Written by MAL Rewrite]

After the victory against Aoba Jousai High, Karasuno High School, once called “a fallen powerhouse, a crow that can’t fly,” has finally reached the climax of the heated Spring tournament. Now, to advance to nationals, the Karasuno team has to defeat the powerhouse Shiratorizawa Academy. Karasuno’s greatest hurdle is their adversary’s ace, Wakatoshi Ushijima, the number one player in the Miyagi Prefecture, and one of the country’s top three aces.
 
Only the strongest team will make it to the national tournament. Since this match is the third-year players’ last chance to qualify for nationals, Karasuno has to use everything they learned during the training camp and prior matches to attain victory. Filled with restlessness and excitement, both teams are determined to come out on top in the third season of Haikyuu!!.
 
[Written by MAL Rewrite]

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