Resiprators offer limited protection against the inhalation of asbestos fibres. FFP3 filters are the only filter type that are suitable for asbestos. All respirators have what is known as a "protection factor", this is assigned by the manufacturer and regulation depending on the filter media condtruction. The protection factor is multiplied by what is known as the "control limit", currently 0.1 fibres per millilitre of air to get the amout of fibre protection.
eg. Full face powered respirator with P3 filter = Protection factor of 40
40x0.1 = 4 f/m air
Bearing in mind that cutting an asbestos cement sheet with a mechanical saw could release around 20 f/m air, you can see that this exceeds the protection of the respirator.
Half masks, both disposable and reusable have a Protection factor of 20, half as much as the powered full face.