ἐγείρω (egeirō)

The Greek word ἐγείρω (egeirō) can mean to “arise” but also according to Thayer’s lexicon, “to come before the public, to appear” and “to cause to appear, bring before the public (any one who is to attract the attention of men).”

In the context of Jesus’ statements referring to appearing after three days - Jesus is speaking of his body’s death (θάνατος (thanatos)) rather than his own death: As Jesus also said:
"Do not be afraid of those who kill the body but cannot kill the soul.” (Matt. 10:28 NIV)
Furthermore, we know that Jesus’ body did not rise. For example, we find this verse in Luke:
After Jesus called out again with a loud voice, his spirit departed. (Matt. 27:50)
Rather, Jesus did not appear to them in his body after his body was murdered:
Afterward Jesus appeared in a different form to two of them while they were walking in the country. (Mark 16:12)
We also find in all four Gospels that Jesus was not immediately recognized when he appeared to them.

One might ask about how Jesus could show his disciples his holes in his hands and also some flesh during his visit in Luke. One would counter that if it was Jesus' dead physical body, then those holes and the flesh would have been decomposing after three days. Rather, Jesus illustrated to them that he was the same person by showing them a facsimile of his body. It was certainly a stunning miracle - but Jesus performed many miracles.

But this doesn't mean that Jesus rose in his physical body and that physical body that died on the cross - from which his spirit left - was walking around three days later. Jesus' spirit-person rose from the body - ἐγείρω (egeirō) - and he appeared to some of his students.

We also note that Jesus suddenly appeared in their chambers, which were locked. We also find this verse in Luke:

While he was blessing them, he departed from them and was carried up into the spiritual realm. (Luke 24:52)