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Howdy. So, here is the thing - MOZ link crawler is very delayed. They crawl about once a month. Also, as any other crawler, there is a limitation on resources. Therefore there is high chance that simply your link profile is not up-to-date. If all other tools are saying that it's the case, then you are good. As for why your website is not ranking better than competitors - there are so many other signals than links. And the metrics are just metrics. Hope this helps.