Parts War

I think you should give detail on Vocab type information, like, Parts War.
Here is the information. People who are interested in Air Gear but can't watch it or read it, may be interested in the information we provide.

Parts War is a battle between Storm Riders to gain AT parts, emblems, territories or Regalia. They also compete in these battles to advance their team to a higher rank.

A team has to bet something in order to battle. Some teams bet their emblem, which, when lost, means the team must also be disbanded.

There are six classes in the Parts War, ranging from F to A, with a different competition for each rank. These competitions are Dash, Hurdle, Cube, Air, Disk and Balloon.

A team can advance in rank by winning three times in a row against opponents of their own class, or winning once against an opponent of higher class.

Some teams are noted to specialize in certain classes or on certain battlefields. For example, Behemoth and Jiggy specialize in D-Class Cube matches, and Sleeping Forest (Ringo in particular) is significantly more powerful inside the shaft of the Trophaeum
The pyramid of Parts War classes.

Basic Classes

These classes teach new riders basic movements for them to learn AT's. Although these classes are considered basic, even high-level Storm Riders participate in them frequently.

F - Dash

Movement taught - "Run". Dash is a simple race to a finish line; the person to get there first wins the battle. Dash matches are carried out in a series of one-on-one races, meaning even 2 opposing Storm Riders could engage in a function Dash match (as seen in the battle between Ikki and Ringo).

E - Hurdle

Movement taught - "Avoid Obstacles". Hurdle incorporates the same concepts present in F-Class Dash matches, meaning one simply has to reach the finish line to win. However, to make things more difficult, large obstacles such as buildings or wide gaps are added to require more skilled AT usage.

D - Cube

Movement taught - "Manage to Use Wall Surfaces". The focus of the majority of Cube matches is one-on-one combat within an enclosed space. However, some battlefields may allow for larger scale combat, as seen during Kogarasumaru's match against Behemoth.

C - Air

Movement taught - "Jump". Air consists of ten platforms, each with a specific number. After a certain amount of time set at the start of the battle, these platforms are successively knocked down in random order. This means that riders must fight against the other team in order to gain solid footing. The last team standing wins the match. Two arenas for Air battles have been seen: the Animal House battle used a "Chupa Chups" arena, in which the platforms were themed after different types of candy. Against Sleipnir, jet airplanes were used, greatly adding to the difficulty and danger of the match.
[edit] Advanced Classes

A team needs to win against B-Class to Special A-Class to enter the Advanced Class.

B - Disk

Disk has two different decisive factors. The first is limit to attack. The person with the disk is called the 'disk keeper', and can attack anyone at will. The others cannot attack anyone else besides the disk keeper. If anyoe breaks this rule, a penalty point is given to the other team. The second most important factor in this class is teamwork. If a team does not co-operate, they definitely will not win.

A - Balloon

The highest ranked, and hardest, battle system utilizing the 6 layers between A and F. Whoever takes the balloon with the emblem wins. The rules may look simple, but the difficulty is extremely high. Balloon is a team game usually carried out in 5-to-5 teams (although 6-to-6 has also been seen), where each team is separated into positions:

* Panther - chases the balloon, and is the only member of the team who is allowed to touch it. If any other rider touches the balloon, the team will be disqualified.
* Decoy - lures enemies away, pretending to be the Panther.
* Ultimate - battles the other team.
* Middle - assists the 3 people in front.
* Keeper - stops the enemies attacks.