How did Sai Baba demonstrate his oneness with Lord Vitthal through his interactions with devotees?

Sai Baba consistently demonstrated his unity with Lord Vitthal through various incidents. Chapter 4 recounts how devotees already regarded him as the "living Lord of Pandhari." When Das Ganu requested a vision of Vitthal, Baba assured him it would appear in Shirdi itself, which it did. Baba showed his omniscience regarding Kakasaheb Dixit's private meditation on Vitthal by referring to the deity as "Vitthal Patil." Furthermore, He rebuked Bhagwantrao Kshirsagar for neglecting his family's Vitthal idol, stating, "He never offers food (Naivedya); he keeps me hungry too." These events collectively illustrate that Baba and Vitthal were not separate entities in his teachings.