This image comes from the book Nordens språk med rötter och fötter ("The languages of the Nordic Countries with roots and feet"), published by the Nordic Council and available in the 5 official Scandinavian languages. It's freely available online here: http://eplads.norden.org/nordenssprak/
This particular image is from this chapter: http://eplads.norden.org/nordenssprak/kap2/2a/06.asp?lang=sv
In Norway they're not always so blindly faithful to their written standards that they would perceive it as pronouncing "jeg" as "eg". I think it's more along the lines of "I pronounce it 'eg' in my dialect but I happen to write it as 'jeg' because I use Bokmål".
Bergen is actually a Bokmål stronghold on the West Coast, surrounded by municipalities using Nynorsk.
And while <eg> is definitely a Nynorsk form, <bor> is Bokmål. In nynorsk it's <bur> :)