Fully anonymous in the absolute sense doesn’t really exist, there’s always some fingerprint data floating around, but you can get close enough that tracking you down to a specific location becomes practically impossible. For traffic arbitrage specifically what you actually want is an antidetect browser rather than just a regular private browser, those are built to mask your digital fingerprint entirely and let you assign different proxies to different profiles so each one looks like it’s coming from a completely different device in a completely different country.