Backinks seem indexed but not showing

Hi there, I am still a starter, having about 6 months when I first took action, and I can't understand something about my backlinks.
I have a bunch of backlinks for a website made about 3 months ago that are live and indexed, checked with small seo tools index checker, but they are not showing anywhere.
Not showing in Ahrefs, Majestic, Moz and even google webmaster tools.
I am sure no link juice is passed on my website because it is still 51+ in google for all my keywords. (I am using Moz rank checker).
Anyone knows why is that happening? I simply cannot understand how can they be indexed but not showing anywhere.

Actually you should be happy the links doesn't show up in the backlink crawlers. If the links are indexed this means google knows about them and this is all you need.