
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.

to raise
To increase or raise something, especially prices, taxes, salaries, or a level.
Die Zentralbank hat den Leitzins angehoben.
The central bank raised the key interest rate.

to begin
(elevated) To begin to speak, sing, or complain.
Der Chor hob zu einem feierlichen Gesang an.
The choir began a solemn song.
'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 increase
Erhöhen and anheben can both mean making a price, salary, or level higher. Erhöhen is neutral and broadly applicable, while anheben sounds more like a deliberate adjustment from an existing level. Use erhöhen in general, and anheben especially for consciously decided changes.

Nach den Verhandlungen hob die Firma die Gehälter gezielt an.
After the negotiations, the company deliberately raised salaries.
Der Anbieter musste wegen höherer Kosten den Preis erhöhen.
The provider had to increase the price because of higher costs.