>>11132362when movies did flying stunts and when old TV shows (think Bewitched or Dream of Jeanie) did, they did what is usually called 'wire work.' Fishing line (what a fisherman would use) isn't strong enough for a person, but it's okay for something that supposedly say Tabitha was blinking her nose and grabbing her plush bear from somewhere else in the room and bringing it over to the crib.
You use something like that to have Pete glide or fly between what looks like two buildings, or construction sites, or what have you.
If you go to a place that sells sewing stuff, they also make clear thread, it looks like thin clear plastic. It's far cheaper but not as strong as fishing line. Craft stores like Micheal 's might have it, even dollar stores might.