What is significance/ chashivus of saving at neitz?
The preferred time to daven is exactly when the sun begins to rise over the horizon, as the Posuk says “Yiraucha im shimesh” (Tehillim 75-5). Davening netz or otherwise known as vasikin, (for those who can do it) is an important preference to davening. It is brought in halacha, that even though it is a mitzvah to daven with a minyan, (because the shechina is present and because the teffilah of a tzibbur is much more potent than the teffilah of a single person), nevertheless, a person that regularly daven vasikin is allowed to daven alone if he doesn’t have such a minyan (see Biur Halacha O:CH 58-1 D:H Umtzvah). Tosefos (Brachos 9b D:H Kol) writes that a person that is “masmich geula l’tefillah, and starts davening at netz, (otherwise called vasikin) will not be harmed all that day. Exactly when the sun rises is the beginning of the time to daven shacharis (l’chatchila).
From a hashkafic angle, the significance may be because it says in the posuk (Tehillim 113-3) “Mimizrach shemesh ad mevoah, meulal shem H-shem” We will praise you H-shem from when the sun comes up until it sets, and when a person davens at netz, he is doing just that. The midrash says that as the suns travels it signs praise to H-shem when we daven and start our davening as the sun begins to rise we are in a way davening together with the sun, which is what the posuk Yiraucha im Shemesh, we are fearing H-shem together with the sun.