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There are two main carrier protocols on the internet: TCP and UDP.
On UDP, you can relatively simply show a different IP address in the "sender" field. In that case, any reply won't reach you, but rather be sent to the address you indicated.
In the case of TCP (which is always used for web browsing), IP address spoofing would simply mean that you can't finish the three-way handshake to even start communicating with the server.