The famous vanishing birdcage magic trick is well known for its visually stunning effect. A magician holds a solid birdcage between his palms and shows it to the audience. People are allowed to touch the cage and prove that it is real. But then they are reminded to pay close attention to the cage and do not blink because it happens in a split second. The magician counts one, two and three! The cage is vanished in front of people's naked eyes without a trace. Magician Clarence Slyter was known for making this amazing trick even better in terms of the handling.
The trick is done by pulling a string attached to the compressible birdcage very quickly up the sleeve so that the cage is hidden in the sleeve. Slyter did the trick with an arm pull, too. One of the biggest challenges of the trick is the length of the pulling string. If it is too long, you would not be able to pull the cage strong enough or fast enough. If it is too short, the cage is not free enough to move and feels stiff and unnatural. Slyter handled that with a reel which can be activated to shorten excessive string when needed.
For objects smaller and lighter than a cage, a props commonly used by magicians is an elastic pull. One popular model is called the 'Raven'. In fact, David Blaine used it to vanish a coin on the back of the audience's hand. The secret of it is an elastic cord fixed inside his jacket with another end attached to a magnet. At the beginning of the trick, David Blaine holds the magnet in his right hand secretly with a small fish string. A coin is placed on the back of the audience's hand. As David Blaine's hand is waved over the coin, the magnet attracted the coin and at the same time he releases the string so that the coin and the magnet fly back inside his jacket. His both hands can then be shown empty and the coin vanished into thin air.
Classic magicians wearing tux on stages have been using this same principle for ages. One example is the Chimney Vanish. A colored silk is placed inside a transparent tube. The tube is shown to the spectators with the silk clearly visible inside. The magician shouts 'hoop!' and the silk is gone. This is elegant but not as magical as David Blaine.
Rather than an elastic cord, some magician uses a retraction reel to do the trick. The reel is constructed with a strong spring inside. An inelastic cord is looped onto the reel. The cord is pulled out for use and stuck by a catch so that it does not spring back. The handkerchief attached to the cord is displayed and manipulated in any desired way. When the magician is ready, the cord is pulled again and the catch is released. The handkerchief then goes up the sleeve likewise.
The conventional square cage is not the only object that has been vanished by means of a pull in the sleeve. There have been round cages, lamps and other large objects, all collapsible, which have gone up the sleeve powered by the arm pull. The exact reverse of the old decanter trick, the spider web and many other appearances can be made to apply to similar vanishes. So may be reversed also adaptations of the several gravity applications, or the revolving panel.