Please describe the "at least two transients" in detail. When do they occur? How long are they? What voltage? What instrument are you using to measure them?
When the chip first receives power all digital I/O pins are reset to INPUT. Because of the high impedance of inputs the pin is left to float.
If the reset was manual (pushing the button) the Arduino UNO bootloader sets Pin 13 to OUTPUT and the reset had cleared the data register so the pin should switch from floating to LOW. The bootloader then turns Pin 13 on and off six times (3 blinks of the LED).
When control passes the the Blink sketch the pinMode() in setup() sets Pin 13 to OUTPUT but since it is already an output that should not cause any transients. The loop() function then almost immediately turns Pin 13 HIGH and the blinking sequence starts.
Connecting with Serial Monitor will cause a Reset which may introduce more transients.