I take it you don't like that gif productionhead, so I will give you something that you you may like.
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Based on my limited SEO experience from years ago I didn't notice any effects a shared analytics/webmaster account would have on my sites. Things might have changed in regard to this though.
I have two sites, A is the money site and B is a site that made for linking to A.
A site and B site has a unique IP.
But they are using the same google analytics account and same google webmaster account - Do you think it's a problem?