Cor Zonneveld you made such beautiful photos!
Really it is very common to see this behaviour, at least, here when I spotted them. I will try to verify if the kind of materials are the same. And if I find anything curious I will let know here.

I suspect that your Anthrax species is in fact Anthrax trifasciatus.

Cor

This is fascinating. I love to watch beeflies, so will also be watching for them using different substances now.

Hmm, since saw-dust is not exactly a naturally occuring substance, I wonder what the flies normally use. Perhaps dust from wood-boring insects? It would be good for visual & chemical camouflage purposes.

@Kahis: I pressed N Evenhuis to come up with an ID, although he's not familiar with European fauna; for that reasosn the ID is provisional. What is the difference between varius and trifasciatus? The latter name sounds like : having three stripes, but it is not clear where these would be...

With saw-dust I actually meant the dust from wood-boring insects! All the dust on the photographds is from wood-boring insects, I believe, but I don't know an English word to make the distinction...

Cor

The word you need in English is 'frass'. This means both the sawdust produced by insect wood boring activity and the sawdust like excrement of wood consuming insects.

Thanks Susan! I'll try to remember...

Well, I am hardly the best to talk about Bombylidae, but ...

I've understood that just one isolated spot in the other part of the wing is typical for trifasciatus; in varius both outer cross-veins have spots.

frass is also used as a term in leafminers (Lepidoptera, Hymenoptera, Diptera,...). There frass are the excrements of the larvae that can be seen when the leafmine is hold against the light. The specific place, shape & color of the frass can be important in determination.
look here for leaf mines of Diptera...

Kahis has convinced me that the shown Anthrax is indeed trifasciatus.