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Due to the scope of the Internet it takes a search engines bandwidth to be able to crawl the entire web. SEO moz hits about the top twenty five percent of links. If links are more recent, there is a chance they won't show up for 4 to 7 weeks due to the data having to be processed after the crawl and the sites crawled only once a month (you can see the dates on the site). Majestic SEO offers a decent free service for your own sites, and the monthly if you handle a lot is small medium level is about $50 per month. Even with the free you will see a lot more links and it shows some additional data as well. For the paid, you get historic, etc.