"Out of the Bag" is full of classical allusions, which showcase Heaney's extensive learning and deep knowledge of Greek mythology in particular. These allusions tie Heaney's childhood anecdote to larger cultural narratives about healing and belief. They also emphasize how much more Heaney knows now, as the adult speaker of the poem, than he did when he was a child. He's far more worldly than the young boy who believed the doctor "delivered" newborn babies to the house in a big leather bag. But he's still fascinated by the power of these myths, and he uses them to make vivid connections to his own experiences.
In line 27, for instance, Heaney describes the doctor's eyes as "Hyberborean," or "beyond-the-north-wind blue." According to the ancient Greek author Herodotus, Hyperborea was an evergreen paradise located in the far north. Here, the allusion to Greek myth anticipates Heaney's visit to the shrine at Epidaurus later in the poem. It also stresses how otherworldly—even inhuman—the godlike Doctor Kerlin seemed to young Heaney.
Later, in section II, Heaney identifies two scholars by name: Peter Levi and Robert Graves. He's referring most directly, here, to their writings about healing sites like Lourdes (in France) and Epidaurus (in Greece). But he's also alluding to a larger body of work on myth, including Graves's influential book The White Goddess (1948). He's invoking a scholarly tradition focused on how cultures use storytelling to make sense of history. Knowing this, the reader can better appreciate that Heaney is trying to do the same kind of work in this poem.
In line 39, Heaney alludes to the Greek god of healing, Asclepius, whom he then mentions again in line 49: "When epiphany occurred and you met the god." By referring to Asclepius simply as "the god," Heaney makes him sound all the more mysterious and powerful. Though Asclepius belongs to a whole pantheon of gods, Epidaurus is the place where he reigns supreme. The "temple of Asclepius" at Epidaurus comes up again in lines 73-74, followed by a reference to the goddess "Hygeia," Asclepius's daughter, whose name is the source of the English word "hygiene."