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As a more descriptive answer: no, a domain transfer does not have to mean downtime. As long as the nameservers for your domain have been correctly set at the old registrar and the new registrar, the visitors of your site won't know the difference if your domain has been transferred. If however your domain is transferred first and only after that process is complete you setup the correct records, then your domain will not be showing your website. But that's something easily avoided with most registrars.