google dont index redirect but only pages?

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hello everyone!

i ask this because google dont index only the redirect address but
also and mainly the old server`s page

i have pr3 redirect domain:

i`m going to renovate my website and to move it to other server.

my question is if it will help me to redirect the domain to the new
server or to put a link in the old server to the new site?
currently they are not so much links to this domain, and i want to ask
if i should beiuld links exchange to this domain or to start link
system to the new domain

p.s. the domain is 7 years old


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