What it does
This is an "addition-line ninjutsu" (付加系の忍術, Fuka kei no Ninjutsu) that augments the killing power of a bladed weapon, By adjusting the amount of chakra applied through Chakra Control, the user can freely alter the length and density/"hardness" of the chakra edge, making the attack range and timing difficult to anticipate.
Asuma performs the Flying Swallow with his unique Chakra Blades. He furthermore prefers using wind chakra so that his blades become sharp enough to cut through stone or metal. His daughter, Mirai, is taught an imitation of it many years after his death.
Description
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The Flying Swallow is a piece used in taikyoku shōgi, a variant of the standard shōgi with over 400 pieces.
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Naruto was taught the basics of this technique to aid him in developing the Wind Release: Rasengan, though it is unclear if he actually can use the technique proper beyond learning its foundation.
** Shikamaru applied the principle of this technique with Asuma's chakra blades to develop Shadow Imitation Shuriken Technique, though it is likewise unclear if he can use the technique directly. He understands the form well enough to teach it to Mirai, though he states at the time that he lacks the taijutsu ability to actually use it. -
Although Tō no Sho classifies Flying Swallow as taijutsu, its actual entry describes it as ninjutsu.
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In the Naruto: Ultimate Ninja series, Kakashi's midair string attacks are named "Flying Swallow", "Rising Swallow" (昇燕, Nobori Tsubame), and "Falling/Dropping Swallow" (降燕, Ori Tsubame). When Asuma became playable in Naruto: Ultimate Ninja 3, the Japanese version of the game used "Flying Swallow" in both Kakashi's and Asuma's movesets. However, across both Kakashi and Asuma in the English translations of the games, their respective moves often go back and forth between called "Flying Sparrow" to avoid confusion.
** Even in later games such as the first Storm game, Kakashi still keeps his swallow-naming-motif for some of his named-normal attack string finishers (also passed onto one of Sasuke's string finishers as well).