A sack. The sack, of course, gives the air, but the cat doesn't feel the foothold, and therefore it feels unnecessary fear.
Boxes
They aren't good if they're made of soft cardboard. Heavy, thick boxes are suitable for transporting cats in the short term. Note the size of the box. They should allow the cat to move. Be sure to make a hole in the box to the access for air.
Bags
Bags made of airtight material aren't allowed. There's a large assortment in special stores.There's always a lack of air in bags made of synthetic materials. It's hot in the summer, cats' pads sweat, they begin to breathe faster. In the winter it's cold in the bag. The best variant would be a large carrying-bag, which has a solid bottom and has the grid at the top. the grid should be fixed securely. Put the cat in the bag head-to-grid, then it feels fresh air and will behave calmly. Don't leave the cat alone in the bag itself, don't forget about it.
The best transportation options are wicker baskets and special plastic carryings for animals.
Baskets must have a lid, which is securely fastened.
Carrying
There's a large amount of them at pet stores that you can choose color, size and the right price. The door is fastened securily of such carrying. The cat will feel itself confident and secure. Besides, it'll always be able to see you and the world.
Do not skimp on such things. The health of your pet depends on them.