Early civilizations of india, Greece, Babylon, China and Egypt have progressed in astronomy. Is there any shared knowledge among them and if any how can we find out?
Much of the ancient transmission went through Greece. Astronomical (and other) knowledge was transmitted from Egypt to Greece at least by the time of early Pythagoreans (c. 500 BC), likely earlier. According to some sources, Pythagoras and Democritus visited Egypt personally to study with the priests. There might have been some early transmission from Babylon, such as of the Metonic and Saros cycles. After the Alexander's conquests (c. 320 BC), Babylonian astronomical observations and computational methods (including sexagesimal arithmetic) came to be widely used by Hellenistic astronomers, starting with Hipparchus (c.250 BC), see Babylonian sources. Recently, evidence of Babylon to Hellenistic Egypt transmission came to light, see Ancient Knowledge Transfer: Egyptian Astronomical Instructions based on Babylonian Methods:
"Egyptian astronomers computed the position of the planet Mercury with methods originating from Babylonia. This is proven by a study of two unpublished Egyptian instructional texts from the Ashmolean Museum (Oxford)... The texts date to 1-50 AD and are written in the Demotic language, a late stage of ancient Egyptian, on two ostraca (potsherds). They are the only known texts from Greco-Roman Egypt with instructions for computing astronomical phenomena with Babylonian methods. The instructions correspond exactly to methods invented in Babylonia several centuries earlier (400-300 BC). Surprisingly, the ostraca employ a mathematical formulation not found in Babylonian texts but whose existence has long been suspected by historians of astronomy."
Ptolemy employed Babylonian methods, inherited from Hipparchus, extensively in the Almagest (c.150 AD), the opus magnum of geocentric astronomy. At least parts of the Almagest were known in India by the time of Aryabhata (c.500 AD), see Duke's The Equant in India. China remained isolated until much later, flat Earth beliefs were still current by the time of Jesuit arrival in 1600-s, see Why was China slow to recognise the sphericity of Earth?
The Circulation of Astronomical Knowledge in the Ancient World is a comprehensive scholarly collection, highlights are given in Wikipedia's History of Astronomy.