I changed my wordpress permalink but now I have two Google results for the same page, how to get rid of the old one?

Selected answers from the Dumb SEO Questions Facebook & G+ community.

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  Nishant Desai: If your new pages are crawled you can delete the old pages.  ;But make sure that redirects are working proper.  ;You can test the same by deleting couple of old pages first and check after 3-4 days that it works fine.  ;Also ensure to design a good 404 error page so in any case if there is any broken link, visitor gets something good to view.
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  Benjamin Pusch: Hi! I think I didn't explained well. There are no new and old pages, only new and old links.
  For example, my link structure was:
  Www.domain.com/postname
  NOW it is
  Www.domain.com/category/postname
  Content is the same
  For not getting punished by google I redirected the old links to the New links for not having dead links in the search results
  You understand?:D
• 
  W.E. Jonk: A 301 redirect should be enough. That is, a 301 redirect from the old page to the new page. Although Googlebot can follow multiple redirects it is best practise to have one redirect.
  
  Roughly speaking, Googlebot crawls the web based on PageRank. So it can take some time before Google crawls every page on your site, especially the ones that are quite deep into the site. If G-bot notice a "new" 301 it might come back the next day and the day after to make sure the 301 is valid. But overtime G-bot will notice the 301 and everything will be transferred to the new page. ;Furthermore it common that G-bot crawls the old URL's from time to time to make sure the 301 is still active. So there is no need to remove the 301 after (let's say) a year, just keep them indefinitely. ;
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  Benjamin Pusch: Yeah I understand this. My problem is that the old links are still in the search results although it is only a redirect. Will Google delete those automatically ? Thanks for your answer
• 
  W.E. Jonk: In short, yes the old URL's will be "deleted" or better moved to the new URL's but you have to be patience. And many webmasters report that it can take quite some time. ;
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  Benjamin Pusch: Yeah that's why I was wondering, it's 2 week's ago... Thank you guys :)
• 
  Ecommerce Maker: Sitemap is gather your important url to easy for the crawling and indexing purpose.