Is the word levanta the same in Brazilian and European Portuguese?

No.

While the spelling and the core dictionary meaning of "levanta" are identical in both dialects, there is a difference in typical usage. In Brazilian Portuguese, "levanta" is frequently used as a standalone imperative to mean "get up" (intransitive). In Continental Portuguese, using "levanta" in this way would be considered grammatically incomplete; a Portuguese person would almost always use the reflexive form, "levanta-te." Additionally, certain metaphorical applications of the word in Brazil are replaced by different verbs in Portugal.

Brazilian Portuguese Examples

1. Levanta logo, a aula já começou! (Get up already, class has already started!)
2. Ele levanta a mão para fazer uma pergunta. (He raises his hand to ask a question.)
3. A mãe levanta o bebê com cuidado. (The mother lifts the baby carefully.)
4. Ele levanta o peso sem nenhum esforço. (He lifts the weight without any effort.)
5. Ela sempre levanta o astral de todo mundo. (She always lifts everyone's mood.)

Continental Portuguese Examples

1. Levanta-te logo, a aula já começou! (Get up already, class has already started!)
2. Ele levanta a mão para fazer uma pergunta. (He raises his hand to ask a question.)
3. A mãe levanta o bebé com cuidado. (The mother lifts the baby carefully.)
4. Ele levanta o peso sem nenhum esforço. (He lifts the weight without any effort.)
5. Ela sempre anima toda a gente. (She always cheers everyone up.)