It is similar here depending upon the type of asbestos. We have category I and category II non-friable asbestos materials which are non-regulated and can be removed with less stringent engineering controls, and then we have Regulated Asbestos Containing Materials [RACM] which require significant controls. The personal protection requirements vary depending upon the anticipated risk of exposures but nominally include a respirator, gloves, rubber boots and a disposable coverall with hood.

To explain completely would take far too much room on this page, but if you really need to find out, EPA.gov has a pretty comprehensive site and lays it all out in easy to read language under the air quality section. I think you will find that Europe is far more stringent about asbestos than the US, which permits materials to be classified relative to the possibility of asbestos breaking free from its matrix.