anheben
to lift
To lift something slightly upward or raise it a little.
Er musste den schweren Stein anheben, um darunter zu schauen.
He had to lift the heavy stone to look underneath it.

to lift / raise
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to lift
To lift something slightly upward or raise it a little.
Er musste den schweren Stein anheben, um darunter zu schauen.
He had to lift the heavy stone to look underneath it.

'Anheben' (to lift/raise) is a separable verb. In a main clause, the prefix 'an' comes at the end. In a subordinate clause and in the infinitive with 'zu', the verb stays together.
Er hebt den Deckel vorsichtig an.
He carefully lifts the lid.
You can recognize the meaning of 'anheben' (to lift/raise/begin) from the object. A concrete, physical object is lifted slightly. An abstract value (price, salary) is raised. A song or speech is begun.
Kannst du den Tisch kurz anheben?
Can you lift the table for a moment?
In the meaning 'erhöhen' (to raise/increase), 'anheben' is typically combined with abstract values. Common collocations are: 'die Preise anheben' (to raise prices), 'die Gehälter anheben' (to raise salaries), 'die Steuern anheben' (to raise taxes), or 'das Niveau anheben' (to raise the level).
Die Regierung plant, die Steuern für hohe Einkommen anzuheben.
The government plans to raise taxes for high incomes.
The meaning 'to begin to speak or sing' is elevated and is used mainly in literature or in very formal contexts. It is rare in everyday language.
Der Priester hob die Stimme zum Gebet an.
The priest raised his voice in prayer.
to begin
'beginnen' and 'anheben' can both mean the start of a spoken or vocal action. 'beginnen' is the normal and versatile word: a conversation, a lecture, or a song can begin. 'anheben' in this meaning is elevated in style and rather rare today. It fits especially in fixed or literary expressions when someone begins to speak, sing, or complain. In everyday language, 'beginnen' sounds much more natural. Use 'anheben' only when the style may be deliberately solemn or old-fashioned.

Der Chor hebt nach einem kurzen Moment zu einem alten Lied an.
After a brief moment, the choir begins an old song.
In der Bibliothek beginnt der Gast leise ein Gespräch mit der Kollegin.
In the library, the guest quietly begins a conversation with the colleague.