The TCP three-way handshake is significant for applications that utilize TCP as a transport protocol for several reasons:

1. Connection Establishment: The three-way handshake is used to establish a connection between the client and the server. This ensures that both the sender and receiver are ready for data transmission and have agreed on the parameters of the exchange.

2. Synchronization of Sequence Numbers: It allows both the client and server to synchronize their initial sequence numbers (ISNs) with each other. This is important for the proper ordering of data packets.

3. Avoiding Duplicate Connections: The three-way handshake helps to avoid duplicate connections. This could happen if an old connection request arrives at the server after a new one has been established.

4. Flow Control and Congestion Handling: During the handshake, both sides also agree on parameters such as window size, which is used for flow control and congestion handling.

5. Error Checking: The handshake process also includes error checking to ensure that data is transmitted accurately.

6. Security: The three-way handshake can also be used to establish a secure connection, such as in the case of a TLS handshake.

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