Was the title too cheesy? Guess we'll find out!
Here are some maps for your illustrative pleasure, and my sources are at the bottom.
Right here you can see the Roman/Byzantine and the Persian/Sasanian/Sassanid Empires in around 600 AD. Note also the Avar Khaganate to the north of Rome, and offscreen the Gokturk Khagans (the Turks) north of Persia, their nomadic enemies. Then note the Ghassanids and Lakhmids, their Arab client kingdoms to the south in the Arabian desert. Those are all the big pieces in today's episode.
The Roman/Byzantine Empire, 600 AD
The Persian/Sasanian Empire, with its conquests during the war
The Roman-Persian frontier in Late Antiquity.
Campaigns of the Final War, 611-624
Heraclius, 624-628
SOURCES
Beate, Dignas & Winter Engelbert. Rome and Persia in Late Antiquity: Neighbors and Rivals. Cambridge: Cambridge University Press, 2007.
Crawford, Peter. The War of the Three Gods: Romans, Persians and the Rise of Islam. Barnsley, South Yorkshire: Pen & Sword, 2013.
Daryaee, Touraj. Sasanian Persia: The Rise and Fall of an Empire. New York: I.B. Tauris, 2009.
Graff, David A. The Eurasian Way of War: Military Practice in Seventh-Century China and Byzantium. New York: Routledge, 2016.
Haldon, John. Warfare, State and Society in the Byzantine World, 565–1204. London: UCL Press, 1999.
Howard-Johnston, James. "Heraclius' Persian Campaigns and the Revival of the East Roman Empire, 622-630." War in History 6, Vol. 1 (1999).
Howard-Johnston, James. The Last Great War of Antiquity. Oxford: Oxford University Press, 2021.
Kaegi, Walter Emil. Heraclius: Emperor of Byzantium. Cambridge: Cambridge University Press, 2003.
Luttwak, Edward. The Grand Strategy of the Byzantine Empire. Cambridge, MA: Harvard University Press, 2009.
Norwich, John Julius. A Short History of Byzantium. New York: Vintage Books, 1997.
Treadgold, Warren. Byzantium and Its Army, 284-1081. Redwood City, CA: Stanford University Press, 1998.