In watchmaking, the term flying describes two distinct things that should not be confused: the flying tourbillon and the flyback function. They are different words for different mechanisms, although in certain high-end chronographs they can coexist in the same caliber.
The flying tourbillon is a tourbillon without an upper bridge. The cage that encloses the balance wheel and escapement is anchored only from below, in cantilever, and rotates freely in the void. The concept dates back to 1920: Alfred Helwig, a teacher at the Glashütte School of Watchmaking, eliminated the upper bridge to make the complete rotation of the mechanism visible without visual obstructions. Before him, all tourbillons were enclosed between two bridges. The practical difference compared to the classical tourbillon concerns mainly the weight of the cage — lighter, because one bridge is missing — and visibility from the dial. In terms of gravitational compensation, the physical principle is identical: the cage performs a 360° rotation usually in 60 seconds, carrying the balance wheel through all positions to average out the rate error. Some more elaborate versions mount two hairsprings instead of one, as in H. Moser's HMC 805 caliber, to improve isochronism and shock resistance. There are also multi-axis configurations — three, four — where each additional axis introduces a supplementary plane of rotation; in that case the term flying refers to the main axis, supported from one side only.
The flyback function is instead a chronograph function. It allows you to reset and restart the count with a single button press, without stopping the hand first and then starting again. It originated in aeronautical and military environments, where timing successive segments does not allow for dead time. In a normal chronograph you need three operations — stop, reset, start — here only one is needed. In some sources flyback appears combined with the column wheel, which manages the sequence of commands more precisely compared to the traditional heart cam.
From my workbench I notice that many clients use flying to indicate any tourbillon with an opening on the dial: this is not correct. A tourbillon visible through a window can be classical. The flying tourbillon is recognized by the absence of the upper bridge: the cage appears suspended in nothing, and if you look at it from the side you can see there is nothing above it.