LTM order of operation

I am looking for the process once a TCP request arrives at a VIP, what is the flow process until the request make it to the pool member (backend server)

it depends on what profiles you have applied to the virtual. For example, with a fastL4 profile on a tcp connection, the handshake to the server will occur as soon as the handshake with the client has completed, whereas with a tcp profile, the handshake is not completed to the server until the first request is made on a successful tcp connection. That is, of course, unless oneconnect is enabled, and the bigip has established the tcp session...

There are many considerations for the process.

I think this SOL would be helpful.

sol8082: Overview of TCP connection setup for BIG-IP LTM virtual server types http://support.f5.com/kb/en-us/solutions/public/8000/000/sol8082.html

Note I'm working on an up to date flow diagram, would love some feedback: https://devcentral.f5.com/questions/tcp-traffic-path-diagram