1. Simultaneous Open
It's possible for two applications to send a SYN to each other to start a TCP connection, although the possibility is small, because both sides have to know which port on the other side to send to. This process is called "Simultaneous Open", or "simultaneous active open on both sides".
For example: An application at host A uses 7777 as the local port and connects to port 8888 on host B. At the same time, an application at host B uses 8888 as the local port and connects to port 7777 on host A. This is "Simultaneous Open".
Here is another example: The Telnet client at host A connects to the Telnet server at host B. At the same time, the Telnet client at host B connects to the Telnet server at host A.
Be careful. This time, it's not "Simultaneous Open" because the two Telnet servers on both sides do "passive open" instead of "active open". There are actually two TCP connections, instead of one in "Simultaneous Open".
TCP is specially designed to deal with "Simultaneous Open", during which only one TCP connection is established, not two. The state transitions are shown in the following figure:
During "Simultaneous Open", 4 packets are exchanged, 1 packet more than in normal situations.
2. Simultaneous Close
It's permitted in TCP for both sides to do "active close", which is called "Simultaneous Close". The state transitions are shown in the following figure:
During "Simultaneous Close", 4 packets are exchanged, the same as in normal situations.